phantom

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: rikpratik.sengupta@gmail.com(RS)) Table of Links Abstract and Intro
The cosmological model
Discussion
Acknowledgments
References Abstract Keywords: oscillating universe, braneworld, bounce, turnaround, phantom. 1. Introduction The standard big bang model of cosmology is plagued by an initial singularity (at time t = 0), where the Friedmann equations describing the time evolution of the universe fails to render a plausible physical description of the space-time dynamics due to the diverging Hubble parameter H, which is a consequence of the infinitely large energy density prevailing in the very early universe. The scalar curvature R also diverges, implying that the initial singularity is a curvature singularity of the Ricci type, which are characterized by diverging energy densities. As shown in their famous singularity theorems by Hawking and Penrose, the initial big bang singularity cannot be avoided in a general relativistic (GR) setup provided the energy conditions are obeyed by matter filling up the universe[4, 5]. One of the key problems of the standard inflationary cosmology, besidies the ambiguity regarding the nature of the inflaton field is that, within the GR framework, inflation can not be past eternal[6]. So, if the inflation is preceeded by a radiation dominated phase, then the origin of the universe is singular. However, today many cosmologists are unhappy about the initial singularity and consider it to be a limitation of GR to describe space-times involving very large energy densities. If there is no big bang, then the possibilities are that the universe either experiences a quantum creation where there is a quantum mechanical tunelling into an inflationary phase, or it may be that the universe existed for an eternally long time in a quasi static state followed by an emergent inflationary phase, or there is a non-singular bounce replacing the singular big bang prior to which the universe contracts and following which the universe expands. In the context of GR, the emergent and bouncing scenarios can be realised effectively only for a spatially closed universe (k = 1). A fully consistent treatment of the first possibility considering quantum creation will most probably require a quantum gravity (QG) treatment. However, there is no fully understood and developed QG theory at the moment and the two most accepted theories being worked on in this context are M-theory[7] involving extra dimensions and Loop Quantum Gravity (LQG)[8]. M- theory requires eleven space-time dimension for its quantum consistency while LQG quantizes space-time itself in the usual four dimensions. Effective theories from both the scenarios have become popular in recent times in the form of the extra dimensional braneworld models[9, 10] and the effective loop quantum cosmology (LQC)[11, 12] models. It is interesting to note that although the premises of the background QG theories are completely different from each other, there are some similarities and identical features that may be obtained from a class of the effective braneworld and LQC models, that may hint at some hidden correspondance between the two contrasting approaches. In this letter, we shall only talk about models that introduce corrections to standard GR at the ultraviolet (UV) scale as we are concerned with resolution of the initial singularity. Braneworld models have the feature that our universe is represented by a (3 + 1)-dimensional hypersurface known as the ’brane’ (which are objects appearing in M-theory) embedded in a higher dimensional bulk spacetime. The Randall Sundrum single brane model (RS-II) is one such model with a spacelike extra dimension, indicating that the signature of the bulk space is Lorentzian. If the signature of the bulk deviates from the former, then we can have a bulk signature (−, −, +, +, +) such that the braneworld has a timelike extra dimension. The standard model particles and fields are confined to the brane, while gravity is free to propagate in the bulk. This paper is available on arxiv under CC 4.0 license. Authors: (1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: rikpratik.sengupta@gmail.com(RS)) This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: rikpratik.sengupta@gmail.com(RS)) Table of Links Abstract and Intro The cosmological model Discussion Acknowledgments References Abstract and Intro Abstract and Intro The cosmological model The cosmological model Discussion Discussion Acknowledgments Acknowledgments References References Abstract Keywords : oscillating universe, braneworld, bounce, turnaround, phantom. Keywords 1. Introduction The standard big bang model of cosmology is plagued by an initial singularity (at time t = 0), where the Friedmann equations describing the time evolution of the universe fails to render a plausible physical description of the space-time dynamics due to the diverging Hubble parameter H, which is a consequence of the infinitely large energy density prevailing in the very early universe. The scalar curvature R also diverges, implying that the initial singularity is a curvature singularity of the Ricci type, which are characterized by diverging energy densities. As shown in their famous singularity theorems by Hawking and Penrose, the initial big bang singularity cannot be avoided in a general relativistic (GR) setup provided the energy conditions are obeyed by matter filling up the universe[4, 5]. One of the key problems of the standard inflationary cosmology, besidies the ambiguity regarding the nature of the inflaton field is that, within the GR framework, inflation can not be past eternal[6]. So, if the inflation is preceeded by a radiation dominated phase, then the origin of the universe is singular. However, today many cosmologists are unhappy about the initial singularity and consider it to be a limitation of GR to describe space-times involving very large energy densities. If there is no big bang, then the possibilities are that the universe either experiences a quantum creation where there is a quantum mechanical tunelling into an inflationary phase, or it may be that the universe existed for an eternally long time in a quasi static state followed by an emergent inflationary phase, or there is a non-singular bounce replacing the singular big bang prior to which the universe contracts and following which the universe expands. In the context of GR, the emergent and bouncing scenarios can be realised effectively only for a spatially closed universe (k = 1). A fully consistent treatment of the first possibility considering quantum creation will most probably require a quantum gravity (QG) treatment. However, there is no fully understood and developed QG theory at the moment and the two most accepted theories being worked on in this context are M-theory[7] involving extra dimensions and Loop Quantum Gravity (LQG)[8]. M- theory requires eleven space-time dimension for its quantum consistency while LQG quantizes space-time itself in the usual four dimensions. Effective theories from both the scenarios have become popular in recent times in the form of the extra dimensional braneworld models[9, 10] and the effective loop quantum cosmology (LQC)[11, 12] models. It is interesting to note that although the premises of the background QG theories are completely different from each other, there are some similarities and identical features that may be obtained from a class of the effective braneworld and LQC models, that may hint at some hidden correspondance between the two contrasting approaches. In this letter, we shall only talk about models that introduce corrections to standard GR at the ultraviolet (UV) scale as we are concerned with resolution of the initial singularity. Braneworld models have the feature that our universe is represented by a (3 + 1)-dimensional hypersurface known as the ’brane’ (which are objects appearing in M-theory) embedded in a higher dimensional bulk spacetime. The Randall Sundrum single brane model (RS-II) is one such model with a spacelike extra dimension, indicating that the signature of the bulk space is Lorentzian. If the signature of the bulk deviates from the former, then we can have a bulk signature (−, −, +, +, +) such that the braneworld has a timelike extra dimension. The standard model particles and fields are confined to the brane, while gravity is free to propagate in the bulk.

Non-singular Oscillating Cosmology on Randall-Sundrum II: Abstract and Intro

র‌্যান্ডাল-সান্ড্রাম II-এ নন-সিঙ্গুলার অসিলেটিং কসমোলজি: অ্যাবস্ট্রাক্ট এবং ইন্ট্রো

Nicht-singuläre oszillierende Kosmologie auf Randall-Sundrum II: Zusammenfassung und Einführung

Cosmología oscilante no singular en Randall-Sundrum II: resumen e introducción

Cosmologie oscillante non singulière sur Randall-Sundrum II : résumé et introduction

रैंडल-सुंड्रम II पर गैर-विलक्षण दोलन ब्रह्मांड विज्ञान: सार और परिचय

ランドール・サンドラム II における非特異振動宇宙論: 概要と序論

Randall-Sundrum II의 비특이 진동 우주론: 요약 및 소개

Cosmologia Oscilante Não Singular em Randall-Sundrum II: Resumo e Introdução

Несингулярная осциллирующая космология по Рэндаллу-Сундраму II: Аннотация и введение

Randall-Sundrum II'de Tekil Olmayan Salınımlı Kozmoloji: Özet ve Giriş

Vũ trụ dao động không đơn lẻ trên Randall-Sundrum II: Tóm tắt và giới thiệu

Randall-Sundrum II 上的非奇异振荡宇宙学：摘要和简介

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: rikpratik.sengupta@gmail.com(RS)) Table of Links Abstract and Intro
The cosmological model
Discussion
Acknowledgments
References 3. Discussion When the universe is contracting, the energy density grows and ultimately diverges making the scalar curvature and the Hubble parameter to diverge as well. This can be understood by the fact that the scale factor vanishes in the Friedmann equation. Bounce is the mechanism that simply prevents the initial singularity from forming by making the scale factor begin to increase before it can reach zero or making the energy density drop off before it can diverge. The condition for bounce is achieved through ¨a > 0, such that the contracting universe starts expanding. Alternatively, in turnaround, the expanding universe must begin to start contracting so that both the scale factor and energy density do not diverge in the finite future and this can be achieved through the condition ¨a < 0. Both at the bounce and turnaround, the Hubble parameter vanishes rather than diverging. The the scale factor neither reaches zero or infinite value as the effective energy density on the brane remains finite. Thus, the universe transits smoothly through both the bounce and turnaround. For cosmology on the brane, both the mechanisms can be achieved by a minimum of requisite components- a scalar field with an inflationary potential and a DE component that violates the NEC. The problem with the phantom is that such an exotic fluid has a number of theoretical inconsitencies and pathologies at the quantum level that makes their existence questionable. The problem with the future singularities can be cured from the correction term on the brane as we have found, but such a fluid may also lead to the vacuum being unstable. Attempts to construct dynamical scalar field models of the phantom have led to a negative kinetic term[25] that in turn results in quantum instabilities[30]. However, there exists a cosmological model of DE with vanishing Λ where the vacuum energy obtained from the quantization of a free scalar field having low mass is described by a supernegative EoS and the model is free of pathologies at the quantum level[31]. Two problems in general feature in most oscillating cosmology models. We shall discuss them very briefly without going into much details before concluding the letter. The first problem is posed by the continued existence of singular objects like black holes from the area theorems of Hawking. However, before the turnaround leading up to the next bounce (via a contraction phase) in a phantom dominated universe, such structures may well be dissolved due to the extremely large gravitationally repulsive effects[32], thus being prevented from disrupting the evolution of the universe during the contracting phase following the turnaround. Infact, it has been shown that[33] the Hawking area theorems may not hold true if the NEC (ρ + p ≥ 0) is violated, as is the case for a phantom dominated universe. Any surviving remnant microscopic black holes may act as possible dark matter candidates. Moreover, the black hole singularity may also be resolved in the UV corrected picture just like the initial big bang and the big rip singularities and also, there may exist non-singular black hole mimickers like gravastar on the brane[34], leading to a complete resolution of the problem at once. It is worth mentioning in this context that the RSII braneworld has also been used in explaining a recent GW event GW170817[35] and the recent observation of the dark shadow of M87∗ [36]. The second problem is associated with the entropy of the universe, which we think remains the same in a periodic manner after the bounce over each cycle, such that the possible increase in entropy during the expanding phase being compensated by a possible decreasing during the radiation/matter dominated expanding phase. This prevents the enrtopy to increase to infinitely large values limiting the number of cycles. We are however concerned mainly with the bounce and turnaround in a single cycle in this letter. This is the first model that can avert the initial singularity using a single brane approach with a positive brane tension. Braneworlds that have a space-like extra dimension like the one we have considered here are characterized by a positive brane tension (as the effective gravitational constant on the brane needs to be positive to explain the attractive nature of gravity) but such a setup could not resolve the big bang singularity. The non-singular models of brane cosmology till date have either resorted to a single brane with time-like extra dimension where no scalar field has to be invoked to generate the bounce which happens naturally from the cosmological dynamics[10], but the brane tension must be negative for the same reason of obtaining a positive effective gravitational constant, or alternatively, introduce a second braneworld with a negative tension parallel to the positive tension brane with finite separation between the branes. The advantage of introducing the parallel negative tension braneworld is two-fold: firstly, negative tension branes have the unique feature of reduced inertia on matter with positive energy density being dumped onto it helping the dynamical realization, and secondly the two brane setup comes with the benefit of a scalar field known as the radion which modulates the inter-brane separation and can both source the bounce at early times as well as behave like phantom dark energy at late times dure to the non-canonical kinetic term evolving to have a negative value[37]. However, there are some tachyonic instabilities associated with negative tension braneworlds which can be possibly resolved in M-theory but has not been explored well enough and requires further formal developments in M-theory (although the properties are really appealing). On the contrary, the ingredients of our model are well explored and the physics is more well understood in terms of a single positive tension brane. The phantom dark energy also does not lead up to the big rip as the quadratic correction to stress energy becomes significant before the singularity can is reached. Also, the scalar field we have used is a physically well motivated one, since it can accommodate the inflationary scenario naturally and its potential need not be reconstructed to explain the generation of seed cosmological perturbations. Most models of cosmology with a nonsingular bounce have either to resort to alternative mechanisms to generate seed perturbations that are not very well understood physically, or have to reconstruct the potential on an ad hoc basis to generate the perturbations, but in our model an inflationary epoch following the bounce driven by the scalar field with an inflationary emergent potential already has all the ingredients responsible for generating these perturbations, and is well understood. We may think of it as a toy model, not because the scenario is physically ill-motivated, but since we have not tested the model against observations. We plan to analyze the primordial observables like the amplitude of scalar perturbations, tensor to scalar ratio and the spectral index and test them against latest observations in a follow up work in the recent future. This paper is available on arxiv under CC 4.0 license. Authors: (1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: rikpratik.sengupta@gmail.com(RS)) This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: rikpratik.sengupta@gmail.com(RS)) Table of Links Abstract and Intro The cosmological model Discussion Acknowledgments References Abstract and Intro Abstract and Intro The cosmological model The cosmological model Discussion Discussion Acknowledgments Acknowledgments References References 3. Discussion When the universe is contracting, the energy density grows and ultimately diverges making the scalar curvature and the Hubble parameter to diverge as well. This can be understood by the fact that the scale factor vanishes in the Friedmann equation. Bounce is the mechanism that simply prevents the initial singularity from forming by making the scale factor begin to increase before it can reach zero or making the energy density drop off before it can diverge. The condition for bounce is achieved through ¨a > 0, such that the contracting universe starts expanding. Alternatively, in turnaround, the expanding universe must begin to start contracting so that both the scale factor and energy density do not diverge in the finite future and this can be achieved through the condition ¨a < 0. Both at the bounce and turnaround, the Hubble parameter vanishes rather than diverging. The the scale factor neither reaches zero or infinite value as the effective energy density on the brane remains finite. Thus, the universe transits smoothly through both the bounce and turnaround. For cosmology on the brane, both the mechanisms can be achieved by a minimum of requisite components- a scalar field with an inflationary potential and a DE component that violates the NEC. The problem with the phantom is that such an exotic fluid has a number of theoretical inconsitencies and pathologies at the quantum level that makes their existence questionable. The problem with the future singularities can be cured from the correction term on the brane as we have found, but such a fluid may also lead to the vacuum being unstable. Attempts to construct dynamical scalar field models of the phantom have led to a negative kinetic term[25] that in turn results in quantum instabilities[30]. However, there exists a cosmological model of DE with vanishing Λ where the vacuum energy obtained from the quantization of a free scalar field having low mass is described by a supernegative EoS and the model is free of pathologies at the quantum level[31]. Two problems in general feature in most oscillating cosmology models. We shall discuss them very briefly without going into much details before concluding the letter. The first problem is posed by the continued existence of singular objects like black holes from the area theorems of Hawking. However, before the turnaround leading up to the next bounce (via a contraction phase) in a phantom dominated universe, such structures may well be dissolved due to the extremely large gravitationally repulsive effects[32], thus being prevented from disrupting the evolution of the universe during the contracting phase following the turnaround. Infact, it has been shown that[33] the Hawking area theorems may not hold true if the NEC (ρ + p ≥ 0) is violated, as is the case for a phantom dominated universe. Any surviving remnant microscopic black holes may act as possible dark matter candidates. Moreover, the black hole singularity may also be resolved in the UV corrected picture just like the initial big bang and the big rip singularities and also, there may exist non-singular black hole mimickers like gravastar on the brane[34], leading to a complete resolution of the problem at once. It is worth mentioning in this context that the RSII braneworld has also been used in explaining a recent GW event GW170817[35] and the recent observation of the dark shadow of M87∗ [36]. The second problem is associated with the entropy of the universe, which we think remains the same in a periodic manner after the bounce over each cycle, such that the possible increase in entropy during the expanding phase being compensated by a possible decreasing during the radiation/matter dominated expanding phase. This prevents the enrtopy to increase to infinitely large values limiting the number of cycles. We are however concerned mainly with the bounce and turnaround in a single cycle in this letter. This is the first model that can avert the initial singularity using a single brane approach with a positive brane tension. Braneworlds that have a space-like extra dimension like the one we have considered here are characterized by a positive brane tension (as the effective gravitational constant on the brane needs to be positive to explain the attractive nature of gravity) but such a setup could not resolve the big bang singularity. The non-singular models of brane cosmology till date have either resorted to a single brane with time-like extra dimension where no scalar field has to be invoked to generate the bounce which happens naturally from the cosmological dynamics[10], but the brane tension must be negative for the same reason of obtaining a positive effective gravitational constant, or alternatively, introduce a second braneworld with a negative tension parallel to the positive tension brane with finite separation between the branes. The advantage of introducing the parallel negative tension braneworld is two-fold: firstly, negative tension branes have the unique feature of reduced inertia on matter with positive energy density being dumped onto it helping the dynamical realization, and secondly the two brane setup comes with the benefit of a scalar field known as the radion which modulates the inter-brane separation and can both source the bounce at early times as well as behave like phantom dark energy at late times dure to the non-canonical kinetic term evolving to have a negative value[37]. However, there are some tachyonic instabilities associated with negative tension braneworlds which can be possibly resolved in M-theory but has not been explored well enough and requires further formal developments in M-theory (although the properties are really appealing). On the contrary, the ingredients of our model are well explored and the physics is more well understood in terms of a single positive tension brane. The phantom dark energy also does not lead up to the big rip as the quadratic correction to stress energy becomes significant before the singularity can is reached. Also, the scalar field we have used is a physically well motivated one, since it can accommodate the inflationary scenario naturally and its potential need not be reconstructed to explain the generation of seed cosmological perturbations. Most models of cosmology with a nonsingular bounce have either to resort to alternative mechanisms to generate seed perturbations that are not very well understood physically, or have to reconstruct the potential on an ad hoc basis to generate the perturbations, but in our model an inflationary epoch following the bounce driven by the scalar field with an inflationary emergent potential already has all the ingredients responsible for generating these perturbations, and is well understood. We may think of it as a toy model, not because the scenario is physically ill-motivated, but since we have not tested the model against observations. We plan to analyze the primordial observables like the amplitude of scalar perturbations, tensor to scalar ratio and the spectral index and test them against latest observations in a follow up work in the recent future.

Non-singular Oscillating Cosmology on Randall-Sundrum II: Discussion

নন-সিঙ্গুলার অসিলেটিং কসমোলজি অন র‍্যান্ডাল-সান্ড্রাম II: আলোচনা

Nicht-singuläre oszillierende Kosmologie auf Randall-Sundrum II: Diskussion

Cosmología oscilante no singular en Randall-Sundrum II: discusión

Cosmologie oscillante non singulière sur Randall-Sundrum II : discussion

रैंडल-सुंड्रम II पर गैर-विलक्षण दोलन ब्रह्मांड विज्ञान: चर्चा

ランドール・サンドラム II における非特異振動宇宙論: 議論

Randall-Sundrum II에 관한 비특이 진동 우주론: 토론

Cosmologia Oscilante Não Singular em Randall-Sundrum II: Discussão

Несингулярная осциллирующая космология на Рэндалле-Сундраме II: обсуждение

Randall-Sundrum II'de Tekil Olmayan Salınımlı Kozmoloji: Tartışma

Vũ trụ dao động không đơn lẻ trên Randall-Sundrum II: Thảo luận

兰德尔-桑德拉姆 II 的非奇异振荡宇宙学：讨论

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: rikpratik.sengupta@gmail.com(RS)) Table of Links Abstract and Intro
The cosmological model
Discussion
Acknowledgments
References 2. The cosmological model The Einstein Field Equations (EFE) on the brane have the general form For the FRW line element describing an isotropic, homogenous universe, the modified EFE on the brane has the form However, in this letter we shall try to construct a novel non-singular cosmological model of oscillating nature on the spatially flat RS II brane with a spacelike extra dimension (ǫ = 1). For a spacelike extra dimension ǫ being positive, the Hubble parameter does not vanish naturally if the energy density ρ rises upto 2σ. So, RS II cosmology does not contain any inherent feature through which a non-singular bounce can be naturally realized. A Weyl curvature singularity due to infinitely large tidal forces at the wormhole throat can be resolved on the RS II brane with ordinary matter[17]. We shall try to induce the bounce using an ingredient that is quite familiar in early universe cosmology and finds application in achieving the inflationary mechanism- a scalar field. The scalar field is minimally coupled meaning that there is no coupling between the scalar field and gravity. In such a model there may exist an infinite number of cycles containing expansion and contraction phases. However, another additional mechanism is required besides a non-singular bounce to generate such an oscillating universe. The universe must begin to contract at late times following an expanding phase before the next cycle begins. This mechanism is known as the turnaround. We shall use two different mechanisms to generate the bounce and turnaround on the flat RS II brane. The time evolution of the scalar field has also been plotted in Figure 1. As evident from the figure (estimating the time of the bounce from Figure 2), negative values of the field play an important role in the bounce. So, from the evolution of the potential, it may be said that the bounce happens for the flatter branch of the potential that leads to an emergent cosmology in a closed relativistic Friedmann universe. We now move on to the late time where the universe is in an accelerating phase. Such a phase has been inferred from astronomical observations[19, 20]. With the discovery of the accelerating universe, there was a resurrection of the Λ-term in cosmology. However, there are certain inconsistencies with the Λ dark energy (DE) that has lead to a wide range of models including quintessence involving scalar fields[21, 22], Chaplygin gas involving fluids with nonlinear equation of states[23, 24] (EoS), the phantom with an exotic EoS[25, 26] and geometrical models which effectively modify the matter sector through geometrical contributions at the infrared (IR) scale[27, 28, 29] but not the real source matter. Here, we have already used a framework in which the geometrical contributions modify the matter sector effectively at the UV scale through the ρ 2 term. If such a term has to be significant in the universe at late times to source a turnaround through its possible non-conventional behaviour (H ∝ ρ), then there has to be a mechanism to make the energy density of the universe grow sufficiently large enough. There is a possibility to achieve this using one of the possible DE candidates that is observationally well favoured-the phantom. The phantom is an exotic fluid with a supernegative EoS (ω < −1) violating the Null Energy condition (NEC), proposed by Caldwell[25] to fit the observational data. The fact tha the phantom fits quite well with the observational data (−1.61 < ω < −0.78) has latter been verified by a number of groups[1, 2, 3]. Again making use of the UV corrected Friedmann equation on the brane, we obtain where α is a constant. We obtain analytical solutions for three different values of the EoS parameter, considering a phantom dominated universe. As we find from Figure 3 on plotiing the scale factor with time, the accelerating phantom dominated universe enters into a contracting phase before the scale factor diverges. Once the universe begins to contract, it is dominated by radiation or matter until the scalar field begins to dominate the universe that causes it to bounce before the scale factor reaches a zero value. So, the scale factor maintains a non zero finite value all along the evolution of the universe, never reaching a singular state. The energy density of the universe has also been plotted in Figure 3 as it evolves with time close to the turnaround. It is found to reach a peak just before the turnaround as it keeps on increasing in the phantom dominated eoch, before falling off again. The energy density is large enough at both early and late times to make the quadratic correction term in the modified EFE significant, but never diverges. It starts dropping following both the bounce and turnaround. This paper is available on arxiv under CC 4.0 license. Authors: (1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: rikpratik.sengupta@gmail.com(RS)) This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: rikpratik.sengupta@gmail.com(RS)) Table of Links Abstract and Intro The cosmological model Discussion Acknowledgments References Abstract and Intro Abstract and Intro The cosmological model The cosmological model Discussion Discussion Acknowledgments Acknowledgments References References 2. The cosmological model The Einstein Field Equations (EFE) on the brane have the general form For the FRW line element describing an isotropic, homogenous universe, the modified EFE on the brane has the form However, in this letter we shall try to construct a novel non-singular cosmological model of oscillating nature on the spatially flat RS II brane with a spacelike extra dimension (ǫ = 1). For a spacelike extra dimension ǫ being positive, the Hubble parameter does not vanish naturally if the energy density ρ rises upto 2σ. So, RS II cosmology does not contain any inherent feature through which a non-singular bounce can be naturally realized. A Weyl curvature singularity due to infinitely large tidal forces at the wormhole throat can be resolved on the RS II brane with ordinary matter[17]. We shall try to induce the bounce using an ingredient that is quite familiar in early universe cosmology and finds application in achieving the inflationary mechanism- a scalar field. The scalar field is minimally coupled meaning that there is no coupling between the scalar field and gravity. In such a model there may exist an infinite number of cycles containing expansion and contraction phases. However, another additional mechanism is required besides a non-singular bounce to generate such an oscillating universe. The universe must begin to contract at late times following an expanding phase before the next cycle begins. This mechanism is known as the turnaround. We shall use two different mechanisms to generate the bounce and turnaround on the flat RS II brane. The time evolution of the scalar field has also been plotted in Figure 1. As evident from the figure (estimating the time of the bounce from Figure 2), negative values of the field play an important role in the bounce. So, from the evolution of the potential, it may be said that the bounce happens for the flatter branch of the potential that leads to an emergent cosmology in a closed relativistic Friedmann universe. We now move on to the late time where the universe is in an accelerating phase. Such a phase has been inferred from astronomical observations[19, 20]. With the discovery of the accelerating universe, there was a resurrection of the Λ-term in cosmology. However, there are certain inconsistencies with the Λ dark energy (DE) that has lead to a wide range of models including quintessence involving scalar fields[21, 22], Chaplygin gas involving fluids with nonlinear equation of states[23, 24] (EoS), the phantom with an exotic EoS[25, 26] and geometrical models which effectively modify the matter sector through geometrical contributions at the infrared (IR) scale[27, 28, 29] but not the real source matter. Here, we have already used a framework in which the geometrical contributions modify the matter sector effectively at the UV scale through the ρ 2 term. If such a term has to be significant in the universe at late times to source a turnaround through its possible non-conventional behaviour (H ∝ ρ), then there has to be a mechanism to make the energy density of the universe grow sufficiently large enough. There is a possibility to achieve this using one of the possible DE candidates that is observationally well favoured-the phantom. The phantom is an exotic fluid with a supernegative EoS (ω < −1) violating the Null Energy condition (NEC), proposed by Caldwell[25] to fit the observational data. The fact tha the phantom fits quite well with the observational data (−1.61 < ω < −0.78) has latter been verified by a number of groups[1, 2, 3]. Again making use of the UV corrected Friedmann equation on the brane, we obtain where α is a constant. We obtain analytical solutions for three different values of the EoS parameter, considering a phantom dominated universe. As we find from Figure 3 on plotiing the scale factor with time, the accelerating phantom dominated universe enters into a contracting phase before the scale factor diverges. Once the universe begins to contract, it is dominated by radiation or matter until the scalar field begins to dominate the universe that causes it to bounce before the scale factor reaches a zero value. So, the scale factor maintains a non zero finite value all along the evolution of the universe, never reaching a singular state. The energy density of the universe has also been plotted in Figure 3 as it evolves with time close to the turnaround. It is found to reach a peak just before the turnaround as it keeps on increasing in the phantom dominated eoch, before falling off again. The energy density is large enough at both early and late times to make the quadratic correction term in the modified EFE significant, but never diverges. It starts dropping following both the bounce and turnaround.

Non-singular Oscillating Cosmology on Randall-Sundrum II: The cosmological model

র‍্যান্ডাল-সান্ড্রাম II-তে অ-একবচন অসিলেটিং কসমোলজি: মহাজাগতিক মডেল

Nicht-singuläre oszillierende Kosmologie nach Randall-Sundrum II: Das kosmologische Modell

Cosmología oscilante no singular en Randall-Sundrum II: el modelo cosmológico

Cosmologie oscillante non singulière sur Randall-Sundrum II : le modèle cosmologique

रैंडल-सुंड्रम II पर गैर-विलक्षण दोलन ब्रह्मांड विज्ञान: ब्रह्मांड संबंधी मॉडल

ランドール・サンドラムの非特異振動宇宙論 II: 宇宙論モデル

Randall-Sundrum II의 비특이 진동 우주론: 우주론 모델

Cosmologia Oscilante Não Singular em Randall-Sundrum II: O modelo cosmológico

Несингулярная осциллирующая космология по Рэндаллу-Сундраму II: космологическая модель

Randall-Sundrum II'de Tekil Olmayan Salınımlı Kozmoloji: Kozmolojik model

Vũ trụ dao động không đơn lẻ trên Randall-Sundrum II: Mô hình vũ trụ

基于兰德尔-桑德拉姆的非奇异振荡宇宙学 II：宇宙学模型

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: rikpratik.sengupta@gmail.com(RS)) Table of Links Abstract and Intro
The cosmological model
Discussion
Acknowledgments
References References [1] Knop, R.A., et al. Astrophys.J. 598 102 (2003) [2] Spergel, D.N., et al, Astrophys.J.Suppl. 148 175 (2003) [3] Tegmark, M. et al, Phys. Rev. D 69 103501 (2004) [4] S. W. Hawking, Phys. Rev. Lett. 17 443 (1966). [5] S. W. Hawking and R. Penrose, Proc. Roy. Soc. London A314 529 (1970). [6] A. Borde, A. H Guth and A. Vilenkin, Phys. Rev. Lett. 90 151301 (2003). [7] J. Polchinski, String Theory, Vol. 2, Superstring Theory and Beyond (Cambridge University Press, 1998). [8] R. Gambini and J. Pullin, A First Course in Loop Quantum Gravity (Oxford University Press, 2011) [9] L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999). 10] Y. Shtanov and V. Sahni, Phys. Lett. B 557, 1 (2003) [11] A. Ashtekar, T. Pawlowski and P. Singh, Phys. Rev. D 74, 084003 (2006). [12] P. Singh, Class. Quantum Grav. 26 125005 (2009). [13] G. Efstathiou and S. Gratton, MNRAS Lett. 496 (2020) L91. [14] S. Vagnozzi et al., Phys. Dark Univ. 33 (2021) 100851. [15] S. Vagnozzi, A. Loeb and M. Moresco, Astrophys. J. 908 (2021) 84. [16] S. Dhawan, J. Alsing and S. Vagnozzi, Mon. Not. Roy. Astron. Soc. 506 (2021) L1. [17] R. Sengupta et al., Class. Quant. Grav. 39 105004. [18] G F. R. Ellis, J. Murugan and C. G. Tsagas, Class. Quant. Grav. 21 (2004) 223. [19] S. J. Perlmutter et al., Nature 391 51 (1998). [20] Riess, A.G. et al., Astron. J. 116 1009 (1998). [21] Zlatev, I., Wang, L. and Steinhardt, P.J., Phys. Rev. Lett. 82 896 (1999). [22] Ure˜na-L´opez, L.A. and Liddle, A., Phys. Rev. D 66 083005 (2002). [23] Kamenshchik, A., Moschella, U. and Pasquier, V., Phys. Lett. B 511 265 (2001) [24] U. Debnath, A. Banerjee, and S. Chakraborty, Class. Quant. Grav. 21 (2004) 5609. [25] Caldwell, R.R., Phys. Lett. B 545, 23 (2002) [26] Frampton, P. and Takahashi, T., Phys. Lett. B 557 135 (2003). [27] G. Dvali, G. Gabadadze and M. Porrati, Phys. Lett. B 485 208 (2000) [28] C. Deffayet, G. Dvali, and G. Gabadadze, Phys. Rev. D 65 (2002) 044023. [29] S. Nojiri and S. D. Odintsov, Int. J. Geom. Methods Mod. Phys., 4 (2007) 115. [30] J. M. Cline, S. Jeon and G. D. Moore, Phys. Rev. D70, 043543 (2004) [31] L. Parker and A. Raval, Phys. Rev. Lett. 86, 749 (2001). [32] R. Caldwell, M. Kamionkowski and N. Weinberg, Phys. Rev. Lett. 91 071301 (2003). [33] P. Davies, Annales Poincare Phys. Theor. 49 297 (1988). [34] R. Sengupta et al., Phys. Rev. D 102 (2020) 024037. [35] L. Visinelli, N. Bolis, and S. Vagnozzi, Phys. Rev. D 97, 064039 (2018). [36] S. Vagnozzi and L. Visinelli, Phys. Rev. D 100, 024020 (2019). [37] I. Banerjee, T. Paul and S. Sengupta, JCAP 02, 041 (2021). This paper is available on arxiv under CC 4.0 license. Authors: (1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: rikpratik.sengupta@gmail.com(RS)) This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Rikpratik Sengupta, Department of Physics, Aliah University, Kolkata 700 160, West Bengal, India (E-mail addresses: rikpratik.sengupta@gmail.com(RS)) Table of Links Abstract and Intro The cosmological model Discussion Acknowledgments References Abstract and Intro Abstract and Intro The cosmological model The cosmological model Discussion Discussion Acknowledgments Acknowledgments References References References [1] Knop, R.A., et al. Astrophys.J. 598 102 (2003) [2] Spergel, D.N., et al, Astrophys.J.Suppl. 148 175 (2003) [3] Tegmark, M. et al, Phys. Rev. D 69 103501 (2004) [4] S. W. Hawking, Phys. Rev. Lett. 17 443 (1966). [5] S. W. Hawking and R. Penrose, Proc. Roy. Soc. London A314 529 (1970). [6] A. Borde, A. H Guth and A. Vilenkin, Phys. Rev. Lett. 90 151301 (2003). [7] J. Polchinski, String Theory, Vol. 2, Superstring Theory and Beyond (Cambridge University Press, 1998). [8] R. Gambini and J. Pullin, A First Course in Loop Quantum Gravity (Oxford University Press, 2011) [9] L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999). 10] Y. Shtanov and V. Sahni, Phys. Lett. B 557, 1 (2003) [11] A. Ashtekar, T. Pawlowski and P. Singh, Phys. Rev. D 74, 084003 (2006). [12] P. Singh, Class. Quantum Grav. 26 125005 (2009). [13] G. Efstathiou and S. Gratton, MNRAS Lett. 496 (2020) L91. [14] S. Vagnozzi et al., Phys. Dark Univ. 33 (2021) 100851. [15] S. Vagnozzi, A. Loeb and M. Moresco, Astrophys. J. 908 (2021) 84. [16] S. Dhawan, J. Alsing and S. Vagnozzi, Mon. Not. Roy. Astron. Soc. 506 (2021) L1. [17] R. Sengupta et al., Class. Quant. Grav. 39 105004. [18] G F. R. Ellis, J. Murugan and C. G. Tsagas, Class. Quant. Grav. 21 (2004) 223. [19] S. J. Perlmutter et al., Nature 391 51 (1998). [20] Riess, A.G. et al., Astron. J. 116 1009 (1998). [21] Zlatev, I., Wang, L. and Steinhardt, P.J., Phys. Rev. Lett. 82 896 (1999). [22] Ure˜na-L´opez, L.A. and Liddle, A., Phys. Rev. D 66 083005 (2002). [23] Kamenshchik, A., Moschella, U. and Pasquier, V., Phys. Lett. B 511 265 (2001) [24] U. Debnath, A. Banerjee, and S. Chakraborty, Class. Quant. Grav. 21 (2004) 5609. [25] Caldwell, R.R., Phys. Lett. B 545, 23 (2002) [26] Frampton, P. and Takahashi, T., Phys. Lett. B 557 135 (2003). [27] G. Dvali, G. Gabadadze and M. Porrati, Phys. Lett. B 485 208 (2000) [28] C. Deffayet, G. Dvali, and G. Gabadadze, Phys. Rev. D 65 (2002) 044023. [29] S. Nojiri and S. D. Odintsov, Int. J. Geom. Methods Mod. Phys., 4 (2007) 115. [30] J. M. Cline, S. Jeon and G. D. Moore, Phys. Rev. D70, 043543 (2004) [31] L. Parker and A. Raval, Phys. Rev. Lett. 86, 749 (2001). [32] R. Caldwell, M. Kamionkowski and N. Weinberg, Phys. Rev. Lett. 91 071301 (2003). [33] P. Davies, Annales Poincare Phys. Theor. 49 297 (1988). [34] R. Sengupta et al., Phys. Rev. D 102 (2020) 024037. [35] L. Visinelli, N. Bolis, and S. Vagnozzi, Phys. Rev. D 97, 064039 (2018). [36] S. Vagnozzi and L. Visinelli, Phys. Rev. D 100, 024020 (2019). [37] I. Banerjee, T. Paul and S. Sengupta, JCAP 02, 041 (2021).

Non-singular Oscillating Cosmology on Randall-Sundrum II: References

নন-সিঙ্গুলার অসিলেটিং কসমোলজি অন র‍্যান্ডাল-সান্ড্রাম II: রেফারেন্স

Nicht-singuläre oszillierende Kosmologie auf Randall-Sundrum II: Referenzen

Cosmología oscilante no singular en Randall-Sundrum II: Referencias

Cosmologie oscillante non singulière sur Randall-Sundrum II : références

रैंडल-सुंड्रम II पर गैर-विलक्षण दोलन ब्रह्मांड विज्ञान: संदर्भ

ランドール・サンドラム II における非特異振動宇宙論: 参考文献

Randall-Sundrum II의 비특이 진동 우주론: 참고 자료

Cosmologia Oscilante Não Singular em Randall-Sundrum II: Referências

Несингулярная осциллирующая космология по Рэндаллу-Сундраму II: Ссылки

Randall-Sundrum II'de Tekil Olmayan Salınımlı Kozmoloji: Referanslar

Vũ trụ dao động không đơn lẻ trên Randall-Sundrum II: Tài liệu tham khảo

基于 Randall-Sundrum II 的非奇异振荡宇宙学：参考文献

Kilmeny of the Orchard by L. M. Montgomery, is part of the HackerNoon Books Series. You can jump to any chapter in this book here . A PHANTOM OF DELIGHT CHAPTER V. A PHANTOM OF DELIGHT Shortly before sunset that evening Eric went for a walk. When he did not go to the shore he liked to indulge in long tramps through the Lindsay fields and woods, in the mellowness of “the sweet ‘o the year.” Most of the Lindsay houses were built along the main road, which ran parallel to the shore, or about the stores at “The Corner.” The farms ran back from them into solitudes of woods and pasture lands. Eric struck southwest from the Williamson homestead, in a direction he had not hitherto explored, and walked briskly along, enjoying the witchery of the season all about him in earth and air and sky. He felt it and loved it and yielded to it, as anyone of clean life and sane pulses must do. The spruce wood in which he presently found himself was smitten through with arrows of ruby light from the setting sun. He went through it, walking up a long, purple aisle where the wood-floor was brown and elastic under his feet, and came out beyond it on a scene which surprised him. No house was in sight, but he found himself looking into an orchard; an old orchard, evidently long neglected and forsaken. But an orchard dies hard; and this one, which must have been a very delightful spot once, was delightful still, none the less so for the air of gentle melancholy which seemed to pervade it, the melancholy which invests all places that have once been the scenes of joy and pleasure and young life, and are so no longer, places where hearts have throbbed, and pulses thrilled, and eyes brightened, and merry voices echoed. The ghosts of these things seem to linger in their old haunts through many empty years. The orchard was large and long, enclosed in a tumbledown old fence of longers bleached to a silvery gray in the suns of many lost summers. At regular intervals along the fence were tall, gnarled fir trees, and an evening wind, sweeter than that which blew over the beds of spice from Lebanon, was singing in their tops, an earth-old song with power to carry the soul back to the dawn of time. Eastward, a thick fir wood grew, beginning with tiny treelets just feathering from the grass, and grading up therefrom to the tall veterans of the mid-grove, unbrokenly and evenly, giving the effect of a solid, sloping green wall, so beautifully compact that it looked as if it had been clipped into its velvet surface by art. Most of the orchard was grown over lushly with grass; but at the end where Eric stood there was a square, treeless place which had evidently once served as a homestead garden. Old paths were still visible, bordered by stones and large pebbles. There were two clumps of lilac trees; one blossoming in royal purple, the other in white. Between them was a bed ablow with the starry spikes of June lilies. Their penetrating, haunting fragrance distilled on the dewy air in every soft puff of wind. Along the fence rosebushes grew, but it was as yet too early in the season for roses. Beyond was the orchard proper, three long rows of trees with green avenues between, each tree standing in a wonderful blow of pink and white. The charm of the place took sudden possession of Eric as nothing had ever done before. He was not given to romantic fancies; but the orchard laid hold of him subtly and drew him to itself, and he was never to be quite his own man again. He went into it over one of the broken panels of fence, and so, unknowing, went forward to meet all that life held for him. He walked the length of the orchard’s middle avenue between long, sinuous boughs picked out with delicate, rose-hearted bloom. When he reached its southern boundary he flung himself down in a grassy corner of the fence where another lilac bush grew, with ferns and wild blue violets at its roots. From where he now was he got a glimpse of a house about a quarter of a mile away, its gray gable peering out from a dark spruce wood. It seemed a dull, gloomy, remote place, and he did not know who lived there. He had a wide outlook to the west, over far hazy fields and misty blue intervales. The sun had just set, and the whole world of green meadows beyond swam in golden light. Across a long valley brimmed with shadow were uplands of sunset, and great sky lakes of saffron and rose where a soul might lose itself in colour. The air was very fragrant with the baptism of the dew, and the odours of a bed of wild mint upon which he had trampled. Robins were whistling, clear and sweet and sudden, in the woods all about him. “This is a veritable ‘haunt of ancient peace,’” quoted Eric, looking around with delighted eyes. “I could fall asleep here, dream dreams and see visions. What a sky! Could anything be diviner than that fine crystal eastern blue, and those frail white clouds that look like woven lace? What a dizzying, intoxicating fragrance lilacs have! I wonder if perfume could set a man drunk. Those apple trees now—why, what is that?” Eric started up and listened. Across the mellow stillness, mingled with the croon of the wind in the trees and the flute-like calls of the robins, came a strain of delicious music, so beautiful and fantastic that Eric held his breath in astonishment and delight. Was he dreaming? No, it was real music, the music of a violin played by some hand inspired with the very spirit of harmony. He had never heard anything like it; and, somehow, he felt quite sure that nothing exactly like it ever had been heard before; he believed that that wonderful music was coming straight from the soul of the unseen violinist, and translating itself into those most airy and delicate and exquisite sounds for the first time; the very soul of music, with all sense and earthliness refined away. It was an elusive, haunting melody, strangely suited to the time and place; it had in it the sigh of the wind in the woods, the eerie whispering of the grasses at dewfall, the white thoughts of the June lilies, the rejoicing of the apple blossoms; all the soul of all the old laughter and song and tears and gladness and sobs the orchard had ever known in the lost years; and besides all this, there was in it a pitiful, plaintive cry as of some imprisoned thing calling for freedom and utterance. At first Eric listened as a man spellbound, mutely and motionlessly, lost in wonderment. Then a very natural curiosity overcame him. Who in Lindsay could play a violin like that? And who was playing so here, in this deserted old orchard, of all places in the world? He rose and walked up the long white avenue, going as slowly and silently as possible, for he did not wish to interrupt the player. When he reached the open space of the garden he stopped short in new amazement and was again tempted into thinking he must certainly be dreaming. Under the big branching white lilac tree was an old, sagging, wooden bench; and on this bench a girl was sitting, playing on an old brown violin. Her eyes were on the faraway horizon and she did not see Eric. For a few moments he stood there and looked at her. The pictures she made photographed itself on his vision to the finest detail, never to be blotted from his book of remembrance. To his latest day Eric Marshall will be able to recall vividly that scene as he saw it then—the velvet darkness of the spruce woods, the overarching sky of soft brilliance, the swaying lilac blossoms, and amid it all the girl on the old bench with the violin under her chin. He had, in his twenty-four years of life, met hundreds of pretty women, scores of handsome women, a scant half dozen of really beautiful women. But he knew at once, beyond all possibility of question or doubt, that he had never seen or imagined anything so exquisite as this girl of the orchard. Her loveliness was so perfect that his breath almost went from him in his first delight of it. Her face was oval, marked in every cameo-like line and feature with that expression of absolute, flawless purity, found in the angels and Madonnas of old paintings, a purity that held in it no faintest strain of earthliness. Her head was bare, and her thick, jet-black hair was parted above her forehead and hung in two heavy lustrous braids over her shoulders. Her eyes were of such a blue as Eric had never seen in eyes before, the tint of the sea in the still, calm light that follows after a fine sunset; they were as luminous as the stars that came out over Lindsay Harbour in the afterglow, and were fringed about with very long, soot-black lashes, and arched over by most delicately pencilled dark eyebrows. Her skin was as fine and purely tinted as the heart of a white rose. The collarless dress of pale blue print she wore revealed her smooth, slender throat; her sleeves were rolled up above her elbows and the hand which guided the bow of her violin was perhaps the most beautiful thing about her, perfect in shape and texture, firm and white, with rosy-nailed taper fingers. One long, drooping plume of lilac blossom lightly touched her hair and cast a wavering shadow over the flower-like face beneath it. There was something very child-like about her, and yet at least eighteen sweet years must have gone to the making of her. She seemed to be playing half unconsciously, as if her thoughts were far away in some fair dreamland of the skies. But presently she looked away from “the bourne of sunset,” and her lovely eyes fell on Eric, standing motionless before her in the shadow of the apple tree. The sudden change that swept over her was startling. She sprang to her feet, the music breaking in mid-strain and the bow slipping from her hand to the grass. Every hint of colour fled from her face and she trembled like one of the wind-stirred June lilies. “I beg your pardon,” said Eric hastily. “I am sorry that I have alarmed you. But your music was so beautiful that I did not remember you were not aware of my presence here. Please forgive me.” He stopped in dismay, for he suddenly realized that the expression on the girl’s face was one of terror—not merely the startled alarm of a shy, childlike creature who had thought herself alone, but absolute terror. It was betrayed in her blanched and quivering lips and in the widely distended blue eyes that stared back into his with the expression of some trapped wild thing. It hurt him that any woman should look at him in such a fashion, at him who had always held womanhood in such reverence. “Don’t look so frightened,” he said gently, thinking only of calming her fear, and speaking as he would to a child. “I will not hurt you. You are safe, quite safe.” In his eagerness to reassure her he took an unconscious step forward. Instantly she turned, and, without a sound, fled across the orchard, through a gap in the northern fence and along what seemed to be a lane bordering the fir wood beyond and arched over with wild cherry trees misty white in the gathering gloom. Before Eric could recover his wits she had vanished from his sight among the firs. He stooped and picked up the violin bow, feeling slightly foolish and very much annoyed. “Well, this is a most mysterious thing,” he said, somewhat impatiently. “Am I bewitched? Who was she? WHAT was she? Can it be possible that she is a Lindsay girl? And why in the name of all that’s provoking should she be so frightened at the mere sight of me? I have never thought I was a particularly hideous person, but certainly this adventure has not increased my vanity to any perceptible extent. Perhaps I have wandered into an enchanted orchard, and been outwardly transformed into an ogre. Now that I have come to think of it, there is something quite uncanny about the place. Anything might happen here. It is no common orchard for the production of marketable apples, that is plain to be seen. No, it’s a most unwholesome locality; and the sooner I make my escape from it the better.” He glanced about it with a whimsical smile. The light was fading rapidly and the orchard was full of soft, creeping shadows and silences. It seemed to wink sleepy eyes of impish enjoyment at his perplexity. He laid the violin bow down on the old bench. “Well, there is no use in my following her, and I have no right to do so even if it were of use. But I certainly wish she hadn’t fled in such evident terror. Eyes like hers were never meant to express anything but tenderness and trust. Why—why—WHY was she so frightened? And who—who—WHO—can she be?” All the way home, over fields and pastures that were beginning to be moonlight silvered he pondered the mystery. “Let me see,” he reflected. “Mr. Williamson was describing the Lindsay girls for my benefit the other evening. If I remember rightly he said that there were four handsome ones in the district. What were their names? Florrie Woods, Melissa Foster—no, Melissa Palmer—Emma Scott, and Jennie May Ferguson. Can she be one of them? No, it is a flagrant waste of time and gray matter supposing it. That girl couldn’t be a Florrie or a Melissa or an Emma, while Jennie May is completely out of the question. Well, there is some bewitchment in the affair. Of that I’m convinced. So I’d better forget all about it.” But Eric found that it was impossible to forget all about it. The more he tried to forget, the more keenly and insistently he remembered. The girl’s exquisite face haunted him and the mystery of her tantalized him. True, he knew that, in all likelihood, he might easily solve the problem by asking the Williamsons about her. But somehow, to his own surprise, he found that he shrank from doing this. He felt that it was impossible to ask Robert Williamson and probably have the girl’s name overflowed in a stream of petty gossip concerning her and all her antecedents and collaterals to the third and fourth generation. If he had to ask any one it should be Mrs. Williamson; but he meant to find out the secret for himself if it were at all possible. He had planned to go to the harbour the next evening. One of the lobstermen had promised to take him out cod-fishing. But instead he wandered southwest over the fields again. He found the orchard easily—he had half expected NOT to find it. It was still the same fragrant, grassy, wind-haunted spot. But it had no occupant and the violin bow was gone from the old bench. “Perhaps she tiptoed back here for it by the light o’ the moon,” thought Eric, pleasing his fancy by the vision of a lithe, girlish figure stealing with a beating heart through mingled shadow and moonshine. “I wonder if she will possibly come this evening, or if I have frightened her away for ever. I’ll hide me behind this spruce copse and wait.” Eric waited until dark, but no music sounded through the orchard and no one came to it. The keenness of his disappointment surprised him, nay more, it vexed him. What nonsense to be so worked up because a little girl he had seen for five minutes failed to appear! Where was his common sense, his “gumption,” as old Robert Williamson would have said? Naturally a man liked to look at a pretty face. But was that any reason why he should feel as if life were flat, stale, and unprofitable simply because he could not look at it? He called himself a fool and went home in a petulant mood. Arriving there, he plunged fiercely into solving algebraical equations and working out geometry exercises, determined to put out of his head forthwith all vain imaginings of an enchanted orchard, white in the moonshine, with lilts of elfin music echoing down its long arcades. The next day was Sunday and Eric went to church twice. The Williamson pew was one of the side ones at the top of the church and its occupants practically faced the congregation. Eric looked at every girl and woman in the audience, but he saw nothing of the face which, setting will power and common sense flatly at defiance, haunted his memory like a star. Thomas Gordon was there, sitting alone in his long, empty pew near the top of the building; and Neil Gordon sang in the choir which occupied the front pew of the gallery. He had a powerful and melodious, though untrained voice, which dominated the singing and took the colour out of the weaker, more commonplace tones of the other singers. He was well-dressed in a suit of dark blue serge, with a white collar and tie. But Eric idly thought it did not become him so well as the working clothes in which he had first seen him. He was too obviously dressed up, and he looked coarser and more out of harmony with his surroundings. For two days Eric refused to let himself think of the orchard. Monday evening he went cod-fishing, and Tuesday evening he went up to play checkers with Alexander Tracy. Alexander won all the games so easily that he never had any respect for Eric Marshall again. “Played like a feller whose thoughts were wool gathering,” he complained to his wife. “He’ll never make a checker player—never in this world.” About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. L. M. Montgomery (2004). Kilmeny of the Orchard. Urbana, Illinois: Project Gutenberg. Retrieved https://www.gutenberg.org/cache/epub/5341/pg5341-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org , located at https://www.gutenberg.org/policy/license.html.

A PHANTOM OF DELIGHT

Thuvia, Maid of Mars by Edgar Rice Burroughs, is part of the HackerNoon Books Series. You can jump to any chapter in this book here . THE PHANTOM BOWMEN THE PHANTOM BOWMEN As Jav leaped toward him Carthoris laid his hand upon the hilt of his long-sword. The Lotharian halted. The great apartment was empty save for the four at the dais, yet as Jav stepped back from the menace of the Heliumite’s threatening attitude the latter found himself surrounded by a score of bowmen. From whence had they sprung? Both Carthoris and Thuvia looked their astonishment. Now the former’s sword leaped from its scabbard, and at the same instant the bowmen drew back their slim shafts. Tario had half raised himself upon one elbow. For the first time he saw the full figure of Thuvia, who had been concealed behind the person of Carthoris. “Enough!” cried the jeddak, raising a protesting hand, but at that very instant the sword of the Heliumite cut viciously at its nearest antagonist. As the keen edge reached its goal Carthoris let the point fall to the floor, as with wide eyes he stepped backward in consternation, throwing the back of his left hand across his brow. His steel had cut but empty air—his antagonist had vanished—there were no bowmen in the room! “It is evident that these are strangers,” said Tario to Jav. “Let us first determine that they knowingly affronted us before we take measures for punishment.” Then he turned to Carthoris, but ever his gaze wandered to the perfect lines of Thuvia’s glorious figure, which the harness of a Barsoomian princess accentuated rather than concealed. “Who are you,” he asked, “who knows not the etiquette of the court of the last of jeddaks?” “I am Carthoris, Prince of Helium,” replied the Heliumite. “And this is Thuvia, Princess of Ptarth. In the courts of our fathers men do not prostrate themselves before royalty. Not since the First Born tore their immortal goddess limb from limb have men crawled upon their bellies to any throne upon Barsoom. Now think you that the daughter of one mighty jeddak and the son of another would so humiliate themselves?” Tario looked at Carthoris for a long time. At last he spoke. “There is no other jeddak upon Barsoom than Tario,” he said. “There is no other race than that of Lothar, unless the hordes of Torquas may be dignified by such an appellation. Lotharians are white; your skins are red. There are no women left upon Barsoom. Your companion is a woman.” He half rose from the couch, leaning far forward and pointing an accusing finger at Carthoris. “You are a lie!” he shrieked. “You are both lies, and you dare to come before Tario, last and mightiest of the jeddaks of Barsoom, and assert your reality. Some one shall pay well for this, Jav, and unless I mistake it is yourself who has dared thus flippantly to trifle with the good nature of your jeddak. “Remove the man. Leave the woman. We shall see if both be lies. And later, Jav, you shall suffer for your temerity. There be few of us left, but—Komal must be fed. Go!” Carthoris could see that Jav trembled as he prostrated himself once more before his ruler, and then, rising, turned toward the Prince of Helium. “Come!” he said. “And leave the Princess of Ptarth here alone?” cried Carthoris. Jav brushed closely past him, whispering: “Follow me—he cannot harm her, except to kill; and that he can do whether you remain or not. We had best go now—trust me.” Carthoris did not understand, but something in the urgency of the other’s tone assured him, and so he turned away, but not without a glance toward Thuvia in which he attempted to make her understand that it was in her own interest that he left her. For answer she turned her back full upon him, but not without first throwing him such a look of contempt that brought the scarlet to his cheek. Then he hesitated, but Jav seized him by the wrist. “Come!” he whispered. “Or he will have the bowmen upon you, and this time there will be no escape. Did you not see how futile is your steel against thin air!” Carthoris turned unwillingly to follow. As the two left the room he turned to his companion. “If I may not kill thin air,” he asked, “how, then, shall I fear that thin air may kill me?” “You saw the Torquasians fall before the bowmen?” asked Jav. Carthoris nodded. “So would you fall before them, and without one single chance for self-defence or revenge.” As they talked Jav led Carthoris to a small room in one of the numerous towers of the palace. Here were couches, and Jav bid the Heliumite be seated. For several minutes the Lotharian eyed his prisoner, for such Carthoris now realized himself to be. “I am half convinced that you are real,” he said at last. Carthoris laughed. “Of course I am real,” he said. “What caused you to doubt it? Can you not see me, feel me?” “So may I see and feel the bowmen,” replied Jav, “and yet we all know that they, at least, are not real.” Carthoris showed by the expression of his face his puzzlement at each new reference to the mysterious bowmen—the vanishing soldiery of Lothar. “What, then, may they be?” he asked. “You really do not know?” asked Jav. Carthoris shook his head negatively. “I can almost believe that you have told us the truth and that you are really from another part of Barsoom, or from another world. But tell me, in your own country have you no bowmen to strike terror to the hearts of the green hordesmen as they slay in company with the fierce banths of war?” “We have soldiers,” replied Carthoris. “We of the red race are all soldiers, but we have no bowmen to defend us, such as yours. We defend ourselves.” “You go out and get killed by your enemies!” cried Jav incredulously. “Certainly,” replied Carthoris. “How do the Lotharians?” “You have seen,” replied the other. “We send out our deathless archers—deathless because they are lifeless, existing only in the imaginations of our enemies. It is really our giant minds that defend us, sending out legions of imaginary warriors to materialize before the mind’s eye of the foe. “They see them—they see their bows drawn back—they see their slender arrows speed with unerring precision toward their hearts. And they die—killed by the power of suggestion.” “But the archers that are slain?” exclaimed Carthoris. “You call them deathless, and yet I saw their dead bodies piled high upon the battlefield. How may that be?” “It is but to lend reality to the scene,” replied Jav. “We picture many of our own defenders killed that the Torquasians may not guess that there are really no flesh and blood creatures opposing them. “Once that truth became implanted in their minds, it is the theory of many of us, no longer would they fall prey to the suggestion of the deadly arrows, for greater would be the suggestion of the truth, and the more powerful suggestion would prevail—it is law.” “And the banths?” questioned Carthoris. “They, too, were but creatures of suggestion?” “Some of them were real,” replied Jav. “Those that accompanied the archers in pursuit of the Torquasians were unreal. Like the archers, they never returned, but, having served their purpose, vanished with the bowmen when the rout of the enemy was assured. “Those that remained about the field were real. Those we loosed as scavengers to devour the bodies of the dead of Torquas. This thing is demanded by the realists among us. I am a realist. Tario is an etherealist. “The etherealists maintain that there is no such thing as matter—that all is mind. They say that none of us exists, except in the imagination of his fellows, other than as an intangible, invisible mentality. “According to Tario, it is but necessary that we all unite in imagining that there are no dead Torquasians beneath our walls, and there will be none, nor any need of scavenging banths.” “You, then, do not hold Tario’s beliefs?” asked Carthoris. “In part only,” replied the Lotharian. “I believe, in fact I know, that there are some truly ethereal creatures. Tario is one, I am convinced. He has no existence except in the imaginations of his people. “Of course, it is the contention of all us realists that all etherealists are but figments of the imagination. They contend that no food is necessary, nor do they eat; but any one of the most rudimentary intelligence must realize that food is a necessity to creatures having actual existence.” “Yes,” agreed Carthoris, “not having eaten to-day I can readily agree with you.” “Ah, pardon me,” exclaimed Jav. “Pray be seated and satisfy your hunger,” and with a wave of his hand he indicated a bountifully laden table that had not been there an instant before he spoke. Of that Carthoris was positive, for he had searched the room diligently with his eyes several times. “It is well,” continued Jav, “that you did not fall into the hands of an etherealist. Then, indeed, would you have gone hungry.” “But,” exclaimed Carthoris, “this is not real food—it was not here an instant since, and real food does not materialize out of thin air.” Jav looked hurt. “There is no real food or water in Lothar,” he said; “nor has there been for countless ages. Upon such as you now see before you have we existed since the dawn of history. Upon such, then, may you exist.” “But I thought you were a realist,” exclaimed Carthoris. “Indeed,” cried Jav, “what more realistic than this bounteous feast? It is just here that we differ most from the etherealists. They claim that it is unnecessary to imagine food; but we have found that for the maintenance of life we must thrice daily sit down to hearty meals. “The food that one eats is supposed to undergo certain chemical changes during the process of digestion and assimilation, the result, of course, being the rebuilding of wasted tissue. “Now we all know that mind is all, though we may differ in the interpretation of its various manifestations. Tario maintains that there is no such thing as substance, all being created from the substanceless matter of the brain. “We realists, however, know better. We know that mind has the power to maintain substance even though it may not be able to create substance—the latter is still an open question. And so we know that in order to maintain our physical bodies we must cause all our organs properly to function. “This we accomplish by materializing food-thoughts, and by partaking of the food thus created. We chew, we swallow, we digest. All our organs function precisely as if we had partaken of material food. And what is the result? What must be the result? The chemical changes take place through both direct and indirect suggestion, and we live and thrive.” Carthoris eyed the food before him. It seemed real enough. He lifted a morsel to his lips. There was substance indeed. And flavour as well. Yes, even his palate was deceived. Jav watched him, smiling, as he ate. “Is it not entirely satisfying?” he asked. “I must admit that it is,” replied Carthoris. “But tell me, how does Tario live, and the other etherealists who maintain that food is unnecessary?” Jav scratched his head. “That is a question we often discuss,” he replied. “It is the strongest evidence we have of the non-existence of the etherealists; but who may know other than Komal?” “Who is Komal?” asked Carthoris. “I heard your jeddak speak of him.” Jav bent low toward the ear of the Heliumite, looking fearfully about before he spoke. “Komal is the essence,” he whispered. “Even the etherealists admit that mind itself must have substance in order to transmit to imaginings the appearance of substance. For if there really was no such thing as substance it could not be suggested—what never has been cannot be imagined. Do you follow me?” “I am groping,” replied Carthoris dryly. “So the essence must be substance,” continued Jav. “Komal is the essence of the All, as it were. He is maintained by substance. He eats. He eats the real. To be explicit, he eats the realists. That is Tario’s work. “He says that inasmuch as we maintain that we alone are real we should, to be consistent, admit that we alone are proper food for Komal. Sometimes, as to-day, we find other food for him. He is very fond of Torquasians.” “And Komal is a man?” asked Carthoris. “He is All, I told you,” replied Jav. “I know not how to explain him in words that you will understand. He is the beginning and the end. All life emanates from Komal, since the substance which feeds the brain with imaginings radiates from the body of Komal. “Should Komal cease to eat, all life upon Barsoom would cease to be. He cannot die, but he might cease to eat, and, thus, to radiate.” “And he feeds upon the men and women of your belief?” cried Carthoris. “Women!” exclaimed Jav. “There are no women in Lothar. The last of the Lotharian females perished ages since, upon that cruel and terrible journey across the muddy plains that fringed the half-dried seas, when the green hordes scourged us across the world to this our last hiding-place—our impregnable fortress of Lothar. “Scarce twenty thousand men of all the countless millions of our race lived to reach Lothar. Among us were no women and no children. All these had perished by the way. “As time went on, we, too, were dying and the race fast approaching extinction, when the Great Truth was revealed to us, that mind is all. Many more died before we perfected our powers, but at last we were able to defy death when we fully understood that death was merely a state of mind. “Then came the creation of mind-people, or rather the materialization of imaginings. We first put these to practical use when the Torquasians discovered our retreat, and fortunate for us it was that it required ages of search upon their part before they found the single tiny entrance to the valley of Lothar. “That day we threw our first bowmen against them. The intention was purely to frighten them away by the vast numbers of bowmen which we could muster upon our walls. All Lothar bristled with the bows and arrows of our ethereal host. “But the Torquasians did not frighten. They are lower than the beasts—they know no fear. They rushed upon our walls, and standing upon the shoulders of others they built human approaches to the wall tops, and were on the very point of surging in upon us and overwhelming us. “Not an arrow had been discharged by our bowmen—we did but cause them to run to and fro along the wall top, screaming taunts and threats at the enemy. “Presently I thought to attempt the thing—the great thing. I centred all my mighty intellect upon the bowmen of my own creation—each of us produces and directs as many bowmen as his mentality and imagination is capable of. “I caused them to fit arrows to their bows for the first time. I made them take aim at the hearts of the green men. I made the green men see all this, and then I made them see the arrows fly, and I made them think that the points pierced their hearts. “It was all that was necessary. By hundreds they toppled from our walls, and when my fellows saw what I had done they were quick to follow my example, so that presently the hordes of Torquas had retreated beyond the range of our arrows. “We might have killed them at any distance, but one rule of war we have maintained from the first—the rule of realism. We do nothing, or rather we cause our bowmen to do nothing within sight of the enemy that is beyond the understanding of the foe. Otherwise they might guess the truth, and that would be the end of us. “But after the Torquasians had retreated beyond bowshot, they turned upon us with their terrible rifles, and by constant popping at us made life miserable within our walls. “So then I bethought the scheme to hurl our bowmen through the gates upon them. You have seen this day how well it works. For ages they have come down upon us at intervals, but always with the same results.” “And all this is due to your intellect, Jav?” asked Carthoris. “I should think that you would be high in the councils of your people.” “I am,” replied Jav, proudly. “I am next to Tario.” “But why, then, your cringing manner of approaching the throne?” “Tario demands it. He is jealous of me. He only awaits the slightest excuse to feed me to Komal. He fears that I may some day usurp his power.” Carthoris suddenly sprang from the table. “Jav!” he exclaimed. “I am a beast! Here I have been eating my fill, while the Princess of Ptarth may perchance be still without food. Let us return and find some means of furnishing her with nourishment.” The Lotharian shook his head. “Tario would not permit it,” he said. “He will, doubtless, make an etherealist of her.” “But I must go to her,” insisted Carthoris. “You say that there are no women in Lothar. Then she must be among men, and if this be so I intend to be near where I may defend her if the need arises.” “Tario will have his way,” insisted Jav. “He sent you away and you may not return until he sends for you.” “Then I shall go without waiting to be sent for.” “Do not forget the bowmen,” cautioned Jav. “I do not forget them,” replied Carthoris, but he did not tell Jav that he remembered something else that the Lotharian had let drop—something that was but a conjecture, possibly, and yet one well worth pinning a forlorn hope to, should necessity arise. Carthoris started to leave the room. Jav stepped before him, barring his way. “I have learned to like you, red man,” he said; “but do not forget that Tario is still my jeddak, and that Tario has commanded that you remain here.” Carthoris was about to reply, when there came faintly to the ears of both a woman’s cry for help. With a sweep of his arm the Prince of Helium brushed the Lotharian aside, and with drawn sword sprang into the corridor without. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Edgar Rice Burroughs (1993). Thuvia, Maid of Mars. Urbana, Illinois: Project Gutenberg. Retrieved October 2022 https://www.gutenberg.org/cache/epub/72/pg72-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org , located at https://www.gutenberg.org/policy/license.html.

THE PHANTOM BOWMEN

Tarzan of the Apes by Edgar Rice Burroughs, is part of the HackerNoon Books Series. You can jump to any chapter in this book here . The Fear-Phantom The Fear-Phantom From a lofty perch Tarzan viewed the village of thatched huts across the intervening plantation. He saw that at one point the forest touched the village, and to this spot he made his way, lured by a fever of curiosity to behold animals of his own kind, and to learn more of their ways and view the strange lairs in which they lived. His savage life among the fierce wild brutes of the jungle left no opening for any thought that these could be aught else than enemies. Similarity of form led him into no erroneous conception of the welcome that would be accorded him should he be discovered by these, the first of his own kind he had ever seen. Tarzan of the Apes was no sentimentalist. He knew nothing of the brotherhood of man. All things outside his own tribe were his deadly enemies, with the few exceptions of which Tantor, the elephant, was a marked example. And he realized all this without malice or hatred. To kill was the law of the wild world he knew. Few were his primitive pleasures, but the greatest of these was to hunt and kill, and so he accorded to others the right to cherish the same desires as he, even though he himself might be the object of their hunt. His strange life had left him neither morose nor bloodthirsty. That he joyed in killing, and that he killed with a joyous laugh upon his handsome lips betokened no innate cruelty. He killed for food most often, but, being a man, he sometimes killed for pleasure, a thing which no other animal does; for it has remained for man alone among all creatures to kill senselessly and wantonly for the mere pleasure of inflicting suffering and death. And when he killed for revenge, or in self-defense, he did that also without hysteria, for it was a very businesslike proceeding which admitted of no levity. So it was that now, as he cautiously approached the village of Mbonga, he was quite prepared either to kill or be killed should he be discovered. He proceeded with unwonted stealth, for Kulonga had taught him great respect for the little sharp splinters of wood which dealt death so swiftly and unerringly. At length he came to a great tree, heavy laden with thick foliage and loaded with pendant loops of giant creepers. From this almost impenetrable bower above the village he crouched, looking down upon the scene below him, wondering over every feature of this new, strange life. There were naked children running and playing in the village street. There were women grinding dried plantain in crude stone mortars, while others were fashioning cakes from the powdered flour. Out in the fields he could see still other women hoeing, weeding, or gathering. All wore strange protruding girdles of dried grass about their hips and many were loaded with brass and copper anklets, armlets and bracelets. Around many a dusky neck hung curiously coiled strands of wire, while several were further ornamented by huge nose rings. Tarzan of the Apes looked with growing wonder at these strange creatures. Dozing in the shade he saw several men, while at the extreme outskirts of the clearing he occasionally caught glimpses of armed warriors apparently guarding the village against surprise from an attacking enemy. He noticed that the women alone worked. Nowhere was there evidence of a man tilling the fields or performing any of the homely duties of the village. Finally his eyes rested upon a woman directly beneath him. Before her was a small cauldron standing over a low fire and in it bubbled a thick, reddish, tarry mass. On one side of her lay a quantity of wooden arrows the points of which she dipped into the seething substance, then laying them upon a narrow rack of boughs which stood upon her other side. Tarzan of the Apes was fascinated. Here was the secret of the terrible destructiveness of The Archer’s tiny missiles. He noted the extreme care which the woman took that none of the matter should touch her hands, and once when a particle spattered upon one of her fingers he saw her plunge the member into a vessel of water and quickly rub the tiny stain away with a handful of leaves. Tarzan knew nothing of poison, but his shrewd reasoning told him that it was this deadly stuff that killed, and not the little arrow, which was merely the messenger that carried it into the body of its victim. How he should like to have more of those little death-dealing slivers. If the woman would only leave her work for an instant he could drop down, gather up a handful, and be back in the tree again before she drew three breaths. As he was trying to think out some plan to distract her attention he heard a wild cry from across the clearing. He looked and saw a black warrior standing beneath the very tree in which he had killed the murderer of Kala an hour before. The fellow was shouting and waving his spear above his head. Now and again he would point to something on the ground before him. The village was in an uproar instantly. Armed men rushed from the interior of many a hut and raced madly across the clearing toward the excited sentry. After them trooped the old men, and the women and children until, in a moment, the village was deserted. Tarzan of the Apes knew that they had found the body of his victim, but that interested him far less than the fact that no one remained in the village to prevent his taking a supply of the arrows which lay below him. Quickly and noiselessly he dropped to the ground beside the cauldron of poison. For a moment he stood motionless, his quick, bright eyes scanning the interior of the palisade. No one was in sight. His eyes rested upon the open doorway of a nearby hut. He would take a look within, thought Tarzan, and so, cautiously, he approached the low thatched building. For a moment he stood without, listening intently. There was no sound, and he glided into the semi-darkness of the interior. Weapons hung against the walls—long spears, strangely shaped knives, a couple of narrow shields. In the center of the room was a cooking pot, and at the far end a litter of dry grasses covered by woven mats which evidently served the owners as beds and bedding. Several human skulls lay upon the floor. Tarzan of the Apes felt of each article, hefted the spears, smelled of them, for he “saw” largely through his sensitive and highly trained nostrils. He determined to own one of these long, pointed sticks, but he could not take one on this trip because of the arrows he meant to carry. As he took each article from the walls, he placed it in a pile in the center of the room. On top of all he placed the cooking pot, inverted, and on top of this he laid one of the grinning skulls, upon which he fastened the headdress of the dead Kulonga. Then he stood back, surveyed his work, and grinned. Tarzan of the Apes enjoyed a joke. But now he heard, outside, the sounds of many voices, and long mournful howls, and mighty wailing. He was startled. Had he remained too long? Quickly he reached the doorway and peered down the village street toward the village gate. The natives were not yet in sight, though he could plainly hear them approaching across the plantation. They must be very near. Like a flash he sprang across the opening to the pile of arrows. Gathering up all he could carry under one arm, he overturned the seething cauldron with a kick, and disappeared into the foliage above just as the first of the returning natives entered the gate at the far end of the village street. Then he turned to watch the proceeding below, poised like some wild bird ready to take swift wing at the first sign of danger. The natives filed up the street, four of them bearing the dead body of Kulonga. Behind trailed the women, uttering strange cries and weird lamentation. On they came to the portals of Kulonga’s hut, the very one in which Tarzan had wrought his depredations. Scarcely had half a dozen entered the building ere they came rushing out in wild, jabbering confusion. The others hastened to gather about. There was much excited gesticulating, pointing, and chattering; then several of the warriors approached and peered within. Finally an old fellow with many ornaments of metal about his arms and legs, and a necklace of dried human hands depending upon his chest, entered the hut. It was Mbonga, the king, father of Kulonga. For a few moments all was silent. Then Mbonga emerged, a look of mingled wrath and superstitious fear writ upon his hideous countenance. He spoke a few words to the assembled warriors, and in an instant the men were flying through the little village searching minutely every hut and corner within the palisades. Scarcely had the search commenced than the overturned cauldron was discovered, and with it the theft of the poisoned arrows. Nothing more they found, and it was a thoroughly awed and frightened group of savages which huddled around their king a few moments later. Mbonga could explain nothing of the strange events that had taken place. The finding of the still warm body of Kulonga—on the very verge of their fields and within easy earshot of the village—knifed and stripped at the door of his father’s home, was in itself sufficiently mysterious, but these last awesome discoveries within the village, within the dead Kulonga’s own hut, filled their hearts with dismay, and conjured in their poor brains only the most frightful of superstitious explanations. They stood in little groups, talking in low tones, and ever casting affrighted glances behind them from their great rolling eyes. Tarzan of the Apes watched them for a while from his lofty perch in the great tree. There was much in their demeanor which he could not understand, for of superstition he was ignorant, and of fear of any kind he had but a vague conception. The sun was high in the heavens. Tarzan had not broken fast this day, and it was many miles to where lay the toothsome remains of Horta the boar. So he turned his back upon the village of Mbonga and melted away into the leafy fastness of the forest. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Edgar Rice Burroughs (1993). Tarzan of the Apes. Urbana, Illinois: Project Gutenberg. Retrieved October 2022 https://www.gutenberg.org/cache/epub/78/pg78-images.html This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org , located at https://www.gutenberg.org/policy/license.html .

The Fear-Phantom

Whether you’re a DevOps, SRE, or just a data-driven individual, you’re probably addicted to dashboards and metrics. We look at our metrics to see how our system is doing, whether on the infrastructure, the application, or the business level. We trust our metrics to show us the status of our system and where it misbehaves. But do our metrics show us what really happened? You’d be surprised how often it’s not the case. In this post I will look into the math and mechanics behind metrics, some common misconceptions, what it takes to have accurate metrics, and if there even is such a thing. Metrics essentials Metrics are essentially roll-ups of raw events. During this roll-up process, the events are translated into numerical data points. A simple example is errors occurring in the system, with a simple metric to count the errors. Metrics can also involve multiple variables, such as a count of requests with a response time higher than 1 second. When measured over time, these data points form a . time series Metrics can be of various types, such as Counters, Gauges, and Histograms. are used for the cumulative counting of events, as we saw in the above examples. typically represent the latest value of measurement. And then there are more elaborate types such as that can sample the of metric values, by counting events in configurable “buckets” or “bins”. For example, you may want to understand the memory usage percent segmented by pods across your cluster in given points in time. Counters Gauges Histograms distribution The mechanics of metrics In an ideal world, we would ingest and store all the raw events, and then calculate the metrics on query time. This would allow us to slice and dice the events in any way we need, and ask any ad-hoc questions we desire. In the real world, however, keeping all the raw events for extended periods of time can be prohibitively expensive, due to the high volumes of data. To overcome this, events are frequently rolled up into metrics in the collection pipeline, while discarding the raw events or retaining them for short periods only. This is oftentimes a matter of a simple configuration in your metrics collector agent. In addition to reducing cost, aggregation upon collection can improve the performance of real-time analytics with higher metric transmission and ingestion rates at a higher frequency, and by avoiding heavy aggregations and calculations on query time. The math of metrics in a nutshell This rolling-up process involves some math. We might want to calculate the mean or median of the response times, or maybe a percentile, or an aggregation over a time window. We might also want to roll up multiple events into one composite metric. For example, I may want to calculate the 95th percentile (commonly known as P95) of all the pods of a specific service across my cluster. Even if you don’t like math, you cannot avoid it with metrics. You need to understand the different aggregation functions, and the relation between the question you wish to ask and the metric and aggregate you need in order to answer it. Let’s look at the Average function as an example, as many tend to start there. Averages, by definition, smoothen things up and will be less suitable for flushing out anomalous behavior and outliers. When investigating latency problems, for example, it will be quite useless to look at average metric values, and you’d be better off looking at percentiles. Determine your questions, design your metrics accordingly In a way, you can think about these metrics as a lossy compression, during which we lose data and context from the raw events. If we don’t keep the raw events, then we need to determine upfront what’s important for us. For example, if I only calculate the average value over the data, I will not be able to ask about the P95 (95th percentile) later over the pre-aggregated data. You need to determine what questions you want to answer, what’s important for you, and design your metrics and aggregations accordingly. A common mistake is that people avoid this design phase, and just use the preset metrics and default values provided out of the box with their metrics collector of choice. While you may think these defaults represent some industry standard, these are oftentimes quite legacy, and in most cases won’t be in tune with your specific needs. https://youtu.be/t9hpWv7fVSk?t=555?embedable=true The measurement problem Just like in physics, the measurement problem occurs when we measure a (seemingly) continuous property at discrete intervals, often called the , which determines the This creates a distorted representation, where the metric may not actually reflect the originally measured property. For example, if we measure the CPU utilization every 60 seconds, then any CPU outlier happening between these sampling points will be invisible to us. sampling interval sampling rate. Moreover, in order to draw a consecutive line, visualization tools oftentimes average over consecutive data points, which gives the misleading appearance of a smooth line. On some occasions the opposite can occur, where you can get artifacts in your metrics that aren’t real, like peaks in your metrics that don’t really exist. This can happen when running aggregations within the storage backend, due to the in which the calculation is being made. Mean time to detection The sampling period also influences how fast a change in the system will be visible in the metrics. Most algorithms require five data points to detect a trend. If the sampling interval is 60 sec, then the simple math determines that it will take five minutes (that is, 60 sec X 5 data points) before we see something is wrong. Could you afford to wait 5 minutes to know that your system crashed? Using shorter sampling intervals (i.e. higher sampling rates) will shorten this period and enable us to detect and react faster. Of course, higher sampling rates incur overhead in CPU and storage, so we need to find the configuration that strikes the right balance for our needs. Varying resolution and downscaling A common practice is to save metrics in different resolutions in a tiered approach, to reduce cost. For example, you may want to save the metric every 10 seconds for the first day, but then every 5 minutes for the next week, and perhaps every 1 hour for the month or more ahead. This practice assumes that we need the finest granularity for the near real-time period, which we may need it if there’s an issue in the system, while investigations over longer periods require larger-scale trends. The different granularities can be achieved by downscaling the metrics, namely calculating the less granular metric off of the higher granularity one. While this sounds perfectly reasonable, math can interfere here, as some aggregation functions are not compatible with certain computations, and can therefore not be aggregated later. For example, percentiles are not additive and cannot be summed up. So, following the above example, if you have a P99 percentile sampled with 10 seconds resolution, you can’t roll them up to a 5-minute resolution. It’s important to be cognizant of the compatibility of the aggregation functions, and when using non-compatible functions such as percentiles, to make design decisions about which resolutions we require, and calculate these time series upfront. The varying resolution is not limited only to the time factor. Another example is saving per-pod data, and then wishing to “group by” nodes or clusters. The same constraint applies here, meaning that if we expect to be interested in slicing and dicing a percentile-based metric per node, per region, per namespace, or across the entire cluster, we need to pre-aggregate accordingly. Another approach is to give up the accuracy of measurements to gain compatibility in computation, by using histograms. You can take histograms of a few servers and sum them up, or histograms of several time windows and sum them up, and then to downscale. The problem is that in this case, percentiles will be estimates rather than accurate. It’s also important to note that histograms are more time-consuming in storage and throughput, as every sample is not just a single number but a few samples (one per bucket). Summary Metrics are a powerful way to monitor our applications. But they are not necessarily representative of the actual system’s state. It requires an understanding of the math and nature of metrics, as well as careful design, to make sure our metrics are indeed useful to answer the questions we need. Having access to the raw data in addition to the metrics is always good, as this is ultimately the source of truth. Want to learn more? Check out the OpenObservability Talks episode: on , or . All Metrics Are Wrong, Some Are Useful Spotify Apple Podcasts other podcast apps This article was originally . here

Why Your Monitoring Dashboard May Be Feeding You Phantom Metrics

Por qué su tablero de monitoreo puede estar brindándole métricas fantasma

Pourquoi votre tableau de bord de surveillance peut-il vous fournir des métriques fantômes

आपका मॉनिटरिंग डैशबोर्ड आपको फैंटम मेट्रिक्स क्यों खिला सकता है

モニタリング ダッシュボードがファントム メトリックを提供している理由

Por que seu painel de monitoramento pode estar alimentando você com métricas fantasmas

Tại sao Bảng điều khiển giám sát của bạn có thể cung cấp cho bạn các số liệu ảo

为什么您的监控仪表板可能会为您提供幻象指标

Astounding Stories of Super-Science, January 1930, by Astounding Stories is part of HackerNoon’s Book Blog Post series. You can jump to any chapter in this book here . Phantoms of Reality - Chapter IX: "Alexandre—" Astounding Stories of Super-Science, January 1930: CHAPTER IX. "Alexandre—" Derek turned back to the balcony. It had been a brief interlude. The mob in the garden, the soldiers at the top of the stairway, and the other guards high on the bridge of the tower were all standing gazing. Shouts again arose as Derek appeared. Again he raised his arms. This time his voice rang out. "Silence all of you! I am a friend! Silence!" At first they did not heed him; then someone shouted: "Quiet! Listen to him! Let him talk!" The crowd was bellowing, and then they ceased. The bell was still. In the hush came Derek's voice: "I am a friend. I come from foreign lands, from distant lands of strange people and strange magic." For answer the crowd shouted and milled in confusion. A stone came up and then another. Derek stood immovable, like a statue gazing down at them. "I command you to disperse. You will not? Then look at me! Look at me, all of you. My will is law beyond this king—beyond these palace soldiers—beyond any power you have ever known." Then I knew a part of Derek's purpose! He had pressed the mechanism at his wrist. He stood imperious with upraised arms. The garden was in a tumult, but in a moment it died. A wave of horror swept the crowd. A freezing, incredulous horror. They stood staring, incredulous, silent, swept with a widening wave of horror. The figure of Derek on the balcony was fading, turning luminous. A wraith, a ghost of his menacing shape standing there. It faded until it was almost gone, and then, as he reversed the mechanism, it materialized again. A moment passed, then he stood again solid before them. His voice rang out, "Will you obey me now? I am a friend of the toilers!" They were prostrate before him. There is no fear more terrible than the fear of the supernatural. In all of history there has been in our world no worship more abject than the worship and fear of a primitive people for its supernatural God. On the platform beneath the balcony, the palace soldiers stared up, horrified. Then they too were prostrate before Derek's threatening gestures and commanding voice. I stood watching, listening. And suddenly, from the prostrate crowd, a man leaped up. In the silence his amazed voice carried over the garden. "Alexandre! It is our Prince Alexandre! Our lost prince!" He stood staring at Derek, his arms gesturing to his comrade around him. He shouted it again: "Our rightful king, come back to us! Don't you recognize him? I saw him go! He went like that—fading into a ghost. Ten years ago, when Leonto killed his father and would have killed him had he not escaped!" The crowd was standing up now. They recognized Derek! There was no doubt of it. The garden was ringing with the tumultuous shouts, "Alexandre! Our lost prince has come back to us!" My head was whirling with it. Derek, prince of this realm? I could see that it was true. Escaped from here as a young lad, when his throne was usurped. Returning now, a man, to claim his own. And suddenly he turned and flashed me his smile. The din from the garden drowned his words. The crowd was shouting: "Alexandre! Our lost prince!" The king's guards on the lower platform stood sullen, confused. I heard footsteps behind me. I whirled around. From the room, the group of Rohbar's crimson nobles were rushing toward me! Their swords were out. One of them shouted, "Kill them now! We must kill them and have done!" There were five or six men in the group. They were no more than ten feet away from me. They came leaping. I stood in the window opening, with only my dirk to oppose them. I shouted, "Derek! Derek!" I think I took a step backward. I was out on the balcony. It flashed over me—Derek and I were caught out here! The first of the red cloaked figures came hurtling through the doorway. I leaped to avoid his sword. I saw the others crowding behind him. Then I felt Derek shove me violently aside. I half fell, but recovered myself at the balcony rail. Five of the crimson nobles were on the balcony. Derek confronted them. His aspect made them pause. They stood, with outstretched swords. The garden was silent; the crowd stared up. And in the silence Derek roared, "Get back! All of you, go back inside! Back, or I'll kill you!" In Derek's right hand he held the cylinder outstretched, leveled at the menacing nobles. "Back, I say!" But instead they rushed him. There was a flash. From the cylinder it seemed that a ray spat out, a flash of silver light. It caught the three men who were in advance of the others. Their swords dropped with a clatter to the balcony floor. They stood, transfixed. An instant. Derek's silver ray played upon them. Their red cloaks were painted with its silver sheen. They were shimmering! I gasped, staring. The other nobles, beyond the ray, had fallen back. And they too stood staring in horror. Another instant The three figures wavered. I saw the face of one of them, with the shock of incredulous horror still upon it. A face turning luminous! A face, erased, with only the staring eyes to mark where it had been! There was a moment when the three stricken men stood like shimmering ghosts, with Derek's deadly ray upon them. Then they were gone! It seemed, just as they vanished, that they were falling through the balcony floor.... Derek snapped off his ray. He rasped, "Back into that room, I tell you!" The remaining nobles fled before him. He turned again to the balcony rail. "My people—yes, I am Alexandre—I had not thought you would recognize me so soon. But you are right—the time has come for me to claim my inheritance. And I will rule you justly." His cylinder was still in his hand; he swept a watchful glance behind him. I thought of Rohbar. He was in the next room, with the king. Had they seen this attack upon Derek? They must have heard the crowd shouting, "Alexandre!" It seemed strange they did not appear. I recall now, as I look back to this moment on the balcony, that I suddenly thought of Hope. She had been beside me just before the nobles attacked. I did not see her now. I was startled, but thought of her was driven from my mind. From within the palace a scream sounded. A girl screaming. But it was not Hope's voice. A girl, screaming, and then shouting: "The king is dead!" Derek came rushing at me. "Charlie, that—" We heard it again. "The king is dead!" We hurried into the adjoining room. There was no one to stop us—no one up here now who dared oppose Derek. The terrified nobles in the room fell cringing before him. "Alexandre—spare us! We are loyal to you!" He strode past them. In the adjacent apartment we found the king lying upon the floor. A wound in his throat welled crimson. He had evidently been lying here alone, and had just now been found by a girl who had entered. He was not quite dead. Derek bent over him. He opened his eyes. He gasped faintly: "Rohbar—killed me. Rohbar and that—accursed crimson Sensua...." His voice trailed away. The light went out of his staring eyes. Derek laid him gently back on the floor. And as though already the news of his death had miraculously spread, the bell in the castle tower began tolling. Not clanging now. Tolling, with slow, solemn accent. The crowd evidently recognized it. We could hear the shouts: "Death! Death has come!" Derek's eyes ware blazing as he stood up. "The end, Charlie! I would not have planned this, and yet...." He did not finish. He whirled, rushed back to the other room and to the balcony. The scene was again in confusion the crowd milling, voices shouting: "The king is dead!" At the edge of the garden a woman's shrill, hysterical laughter rose over the din. Derek called, "Yes, the king is dead!" He paused. Then he added, "If you want me—if I have your loyalty—I will claim my throne." A tumult interrupted him. "Alexandre! King Alexandre!" He spread his arms, but he could not silence them. "The king is dead. Long live King Alexandre!" A wave of it swept over the garden, engulfing the castle. At the main entrance Leonto's soldiers stood sullen, listening to it. Derek stood triumphant. His hands were outstretched, palms down. But up on the circular bridge at the top of the tower there was a sudden commotion. The soldiers up there had vanished, moved back within the tower to make room for other figures. I stared amazed, transfixed. A huge man in leather garments was there, with a sword stuck in his wide belt. A man with a bullet head, a heavy face, gazing down.... Rohbar! And held in front of him the slender figure of a girl. Hope! He clutched her, his thick arm encircling her breast. With sinking heart I realized what had happened. Hope had moved away from me. Every one in the room had been intent upon Derek. Rohbar had come quietly in, after murdering the king, had seized Hope, stifled her outcry, and had taken her up into the tower. And I had promised Derek that I would shield this girl from harm! The horror of it—the self-condemnation of it—swept me, froze me to numbness. I could not think; I could only stand and stare. Rohbar held Hope like a shield before him. The low railing hardly reached her knees. A sheer drop to the garden beneath. He held her tightly, and in his free hand I saw his dirk come up menacingly against her white throat. His voice called: "Silent, down there! Alexandre, you traitor! Silence!" Derek stared up. The triumph faded from him. He stared, stricken. The crowd stared. The soldiers on the lower platform ceased their shouting and gazed up at these new actors, come so unexpectedly upon the stage. Again Rohbar called, to the guards this time: "I represent your King Leonto. This Alexandre is a traitor to us all. And he cannot harm me! I defy him. Look at him! I defy him to use his evil weapon upon me!" Derek was silent. A single adverse move and Rohbar's knife would stab into Hope's throat. Derek's ray was powerless. A flash from it would have killed Hope, not Rohbar. The king's soldiers saw Derek's indecision. One of them shouted, "He cannot harm us! Look, he is frightened!" The crowd recognized Hope. They began calling her name. And calling, "Master Rohbar, do not harm our Hope!" "I will not harm her! Not if you do what I tell you! Leave the garden—go quietly! I will deal with this traitor!" He added to the guards, "Go up and seize him! He cannot hurt you! Traitor! Seize him! If he does not yield—if any of this crowd attacks you—then I will kill Hope." Derek stood clinging to the balcony rail. With Rohbar's watchful gaze upon him he did not dare turn or move. I was standing back from the balcony, behind Derek and partly in the room. No one thought of me. No one from outside could see me. And I, who had played no part in this, save that one I had neglected, suddenly saw my role. My cue was sounding. My role to play, here upon this tumultuous stage. I turned back into the dim room. A few frightened men and girls were here. They were all crowding forward, gazing through the windows at the scene outside. No one noticed me, but I saw, with sudden realization, my role to play. I darted across the room, out into the dim, deserted corridor of the castle. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Various. 2012. Astounding Stories of Super-Science, January 1930. Urbana, Illinois: Project Gutenberg. Retrieved May 2022 from https://www.gutenberg.org/files/41481/41481-h/41481-h.htm#Phantoms_of_Reality This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org , located at https://www.gutenberg.org/policy/license.html .

Phantoms of Reality - Chapter IX Alexandre

One of the biggest cliches in the current hype about Web 3.0 is the concept of decentralization. The term has taken on many self-important quasi-philosophical features, such as Enlightenment-era ideals of autonomy, self-determination, and the ultimate subjective: “freedom”. All across the web, you can read articles proclaiming the dawn of “decentralized digital identity”, which just begs the question: is digital identity something that could be decentralized? Setting aside much of the (mostly manufactured) cheerleading for “decentralization” in all forms, I want to focus on how digital identity, almost by definition, could never possibly be decentralized. I believe pretty much the exact opposite is true: digital identity will be the ultimate centralized commodity (perhaps it already is). One of the key features that decentralization zealots rely on is blockchain technology. Despite what some may say, blockchain is not inherently decentralized any more than any other database. It could be argued that it is apt to be even more centralized since blockchain is immutable. Those who have access to an immutable blockchain database could certainly wield a lot of power over the data stored therein. This brings up another question: is your digital identity immutable? What exactly is your digital identity anyway? Digital Identity Digital identity is merely a dataset that is constantly updating and fluctuating. This dataset is a construct, an avatar of you or who you are. These datasets are collections of any scattered behaviors, actions, and interactions you may (or may not) have online with myriad people and organizations. Is that collection WHO you are? Or, isn’t it just a sample of WHAT you have done? Is a pattern the same thing as a person? Maybe this is pedantic, but there is a huge difference between who you are and what you do. For example, if I buy several books on Amazon about true crime and serial killers, does that indicate that I am a criminal, murderer, lawyer, or investigator? If I were to post on Twitter some thoughts and opinions on food prices, does that make me an economist? Herein lies much of the problem with the concept of digital identity: human beings are NOT simple datasets that can be aggregated and put into neat little boxes on any sort of database, whether it be blockchain or whatever. The whole idea of digital identity is an invention of corporations, governments, and non-governmental organizations for purposes of profit and control. Facebook, Twitter, and others seem to revel in the power they have to remove people from their platforms for nearly any reason. They accomplish this through the control they have over your “digital identity”, which can be interpreted and manipulated at will in any context. To think that anyone could somehow achieve autonomous control over their own digital identity is a pure illusion (or more accurately: delusion). Blockchain will not facilitate autonomy over digital identity, as once anything is “written” to the blockchain, it is there permanently. Forever. Blockchain may have some utility in cases of asset ownership and trade, but digital identity is not an “asset” that anyone “owns” or even “possesses”. Digital identity is a phantom that constantly changes depending on the context of where it is being used. There is not going to be decentralization of digital identity, but there will most certainly be more centralization of it. Your credit score, education and medical records, criminal history, online habits, banking and money, and any other data that is inherently quantifiable are not even really “yours”. Unless you want to go live out in a cave somewhere and never interact with another person again, everything you do is inevitably being used as a data commodity. There will be no decentralized blockchain that is free from observation and commodification. The reality is much worse, as the opposite becomes easier: since blockchain cannot be rewritten, your digital identity will likely contain mistakes, errors, and outdated info, and will always be subject to the rule of law. Too much quasi-libertarian nonsense permeates the blockchain space, where these myths of decentralized everything swirl around in an echo chamber. Governments, institutions, and corporations will always use laws and regulations to assert authority over any blockchain-related info. How could it be otherwise? What about the innumerable ways in which you can attempt to mask or manipulate your own digital identity? Do you have different email addresses for different purposes: business, personal, or otherwise? Have you ever used a temporary email account? Do you have an alias? Do you have anything in your background that you would rather some people not know about? Do you think that employers will not have any access to your records just because they are on the blockchain? What about lawyers, judges, and governments? How is it decentralization when entities with these powers and abilities retain such access? This entire issue reminds me of an important distinction within the field of web development: the difference between authentication and authorization. Just because someone’s digital identity or credentials have authorized access to something does not necessarily allow them authorization to any and everything. When logging into a website, you authenticate your digital identity by entering the correct information or data. Once you log in (depending on the situation) you may or may not have authorization to every feature of that site. The situation does not change because now your credentials and records are stored in a blockchain database rather than any other database. You can authenticate who you are in the physical world, but that does not necessarily mean you have the authorization to stop the use of your info. The control over such things as authorization will always be subject to higher-order authorities in any society where there is the rule of law. Decentralization, autonomy, and total revolution is not going to take place via blockchain databases. If only it were so easy.

The Digital Identity Phantom Menace

Stories, News & Mentions about PHANTOM

Phantom’s Stories on HackerNoon