Axion Ray

axionray

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London;
(4) DANIEL GRIN, Haverford College;
(5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro
Methods
Phenomenology
Discussion and Future Work
Conclusion
Acknowledgments and References 2. METHODS In order to model the behavior of extreme axions, we modified axionCAMB to include an arbitrary field potential shape (in our case, a cosine of the form given in Equation 1), and reconfigured the code to sample the extreme starting angles necessary to probe these potentials. We also modified the effective sound speed of the axions after the onset of oscillations to reflect the growth in structure resulting from the tachyonic field dynamics. Lastly, we implemented a computationally-efficient ‘lookup table’ of the axion background fluid evolution in order to speed up the computation of the perturbation equations of motion. The details of implementing extreme axions into axionCAMB are presented below [2]. 2.1. Review of axionCAMB The numerical treatment of axions in axionCAMB is described in detail in Hlozek et al. ˇ (2015), but we review the dynamics of axions here in a potential-agnostic way in order to set up our discussion of modeling extreme axions. In theory, the best way of modeling the dynamics of axion dark matter is to model the behaviour of the field throughout all of cosmic history, and derive all cosmological parameters from those primary variables. However, since this field evolution includes periods of extremely rapid oscillations at late times, simulating this is computationally prohibitive and numerically unstable. Instead, the axion field is modeled directly at early times, but the code switches to a simplified fluid approximation at late times (Hlozek et al. ˇ 2015). This piecewise background evolution could then be called when solving the equations of motion for the fluid perturbations (axion density perturbation δa and axion heat flux u), allowing for efficient and stable computation of the final axion power spectrum. This method is discussed here, building on the discussion in Hu (1998) and Hlozek et al. ˇ (2015). axionCAMB runs through this early pre-oscillatory phase several times in order to determine the proper initial value of the axion field required to produce the desired final axion density, and the time at which it can safely switch back to the free particle CDM solution at late times. It then dynamically evolves these initial conditions (integrating the equation of motion for a field using a Runge-Kutta integrator, Runge 1895) until the field starts to oscillate, at which point it switches over to the known free-particle solution for DM evolution (Hlozek et al. ˇ 2015). This results in a new set of equations of motion for the axion perturbations after the onset of oscillations: The perturbation equations of motion in these two regimes can be used to calculate the evolution of the axion perturbations, and make predictions for cosmological observables such as the MPS or CMB. 2.2. Finely tuned initial conditions Restructuring the initial shooting methods to specify the field starting angle allows us to probe the effects of extreme starting angles in new ways. We can specify starting angles arbitrarily close to π, in order to see the effects of these extremely finely tuned angles on other observables. In addition, when performing MCMC analysis, having the starting angle as a free parameter allows us to impose arbitrary priors on this starting angle. We can use these priors to test the dependence of any constraints on the level of fine tuning of the axion starting angle. 2.3. Modeling the early-oscillatory effective axion sound speed To get a sense of the effects of the anharmonic potential on the axion fluid sound speed, we first solve the axion field perturbation equations of motion, This approximation of the fluid sound speed is shown in red in the lower subplot of Figure 2. In order to approximate the boost in the axion sound speed shown in the field equations without changing the late-time evolution of the perturbations, we modified the vanilla axion fluid sound speed to include a large negative spike just after the onset of oscillations. This negative triangular spike is shown in green in the lower subplot of Figure 2. The width and height of this spike were fit to match the approximate sound speed computed from the field perturbation solution. The width (C1) was fit to the delay in scale factor a between the onset of axion oscillations and the asymptotic sign change in the field solution sound speed. This numerical width was then approximated as a power law function of the scale factor k of the perturbation, depends linearly on the scale factor at the onset of oscillations, which in turn depends on the axion mass, fraction, and starting angle, The power spectrum results for this method can be compared to the literature, where other groups have used the exact field perturbation equations of motion to compute the matter power spectrum for extreme axions, such as Leong et al. (2019). In Figure 3 we can see the comparison in the matter power spectrum for both a vanilla axion and an extreme axion with a starting angle deviating from π by 0.2 degrees, and we find that they are in remarkably close agreement with Leong et al. (2019). However, this close agreement seems to hold best at z = 0, when these power spectra are computed, while the higher redshifts comparison may be more nuanced. Figure 2 suggests that while the exact field solution and the new approximate fluid solution agree at very late times, their evolution at early times are not fully equivalent, so more work may need to be done on this approximation in order to perform comparisons to high-redshift observables. 2.4. Using lookup tables for efficient modeling of field Extending the full field evolution so much later past the onset of oscillations requires far more computational resources than ending the field evolution as soon as oscillations begin. Greater numerical resolution, in both time and possible field potential scale, is also required to integrate these rapidly oscillating variables. With these increases to computational time, the new version of axionCAMB takes around seventy seconds to complete. While this may be feasible when computing a single power spectrum result, this is computationally intensive with which to run an MCMC analysis, which may require tens to hundreds of thousands of separate calls to axionCAMB. 2.5. Summary of changes to axionCAMB In order to model axions with extreme starting angles in a cosine field potential using the computationally efficient field formalism used in axionCAMB, we have introduced a number of modifications to axionCAMB which are explained above, but summarized here. • We replaced the quadratic approximation of the field potential with an arbitrary potential function, currently set to the canonical cosine potential. • We modified the effective axion fluid sound speed to reproduce the growth in structure seen in the exact field perturbation equations of motion. • We precomputed a lookup table for the axion background evolution which significantly reduced the runtime. The result is an accurate modeling of extreme axion background and perturbation evolution for an arbitrary axion mass, density, and starting angle that only takes ∼ 7 seconds to run. This powerful tool can shed new light on the behaviour and detectability of these extreme axion models, as discussed below. 2.6. Data: Ly-α forest estimates of the MPS [2] axionCAMB is in turn based on the cosmological Boltzmann code, CAMB (Lewis & Bridle 2002). [4] A logarithmic dependence for the background field can be derived analytically for the anharmonic corrections to the relic density (Lyth 1992). This paper is available on arxiv under CC 4.0 license. Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro Methods Phenomenology Discussion and Future Work Conclusion Acknowledgments and References Abstract and Intro Abstract and Intro Methods Methods Phenomenology Phenomenology Discussion and Future Work Discussion and Future Work Conclusion Conclusion Acknowledgments and References Acknowledgments and References 2. METHODS In order to model the behavior of extreme axions, we modified axionCAMB to include an arbitrary field potential shape (in our case, a cosine of the form given in Equation 1), and reconfigured the code to sample the extreme starting angles necessary to probe these potentials. We also modified the effective sound speed of the axions after the onset of oscillations to reflect the growth in structure resulting from the tachyonic field dynamics. Lastly, we implemented a computationally-efficient ‘lookup table’ of the axion background fluid evolution in order to speed up the computation of the perturbation equations of motion. The details of implementing extreme axions into axionCAMB are presented below [2]. 2.1. Review of axionCAMB The numerical treatment of axions in axionCAMB is described in detail in Hlozek et al. ˇ (2015), but we review the dynamics of axions here in a potential-agnostic way in order to set up our discussion of modeling extreme axions. In theory, the best way of modeling the dynamics of axion dark matter is to model the behaviour of the field throughout all of cosmic history, and derive all cosmological parameters from those primary variables. However, since this field evolution includes periods of extremely rapid oscillations at late times, simulating this is computationally prohibitive and numerically unstable. Instead, the axion field is modeled directly at early times, but the code switches to a simplified fluid approximation at late times (Hlozek et al. ˇ 2015). This piecewise background evolution could then be called when solving the equations of motion for the fluid perturbations (axion density perturbation δa and axion heat flux u), allowing for efficient and stable computation of the final axion power spectrum. This method is discussed here, building on the discussion in Hu (1998) and Hlozek et al. ˇ (2015). axionCAMB runs through this early pre-oscillatory phase several times in order to determine the proper initial value of the axion field required to produce the desired final axion density, and the time at which it can safely switch back to the free particle CDM solution at late times. It then dynamically evolves these initial conditions (integrating the equation of motion for a field using a Runge-Kutta integrator, Runge 1895) until the field starts to oscillate, at which point it switches over to the known free-particle solution for DM evolution (Hlozek et al. ˇ 2015). This results in a new set of equations of motion for the axion perturbations after the onset of oscillations: The perturbation equations of motion in these two regimes can be used to calculate the evolution of the axion perturbations, and make predictions for cosmological observables such as the MPS or CMB. 2.2. Finely tuned initial conditions Restructuring the initial shooting methods to specify the field starting angle allows us to probe the effects of extreme starting angles in new ways. We can specify starting angles arbitrarily close to π, in order to see the effects of these extremely finely tuned angles on other observables. In addition, when performing MCMC analysis, having the starting angle as a free parameter allows us to impose arbitrary priors on this starting angle. We can use these priors to test the dependence of any constraints on the level of fine tuning of the axion starting angle. 2.3. Modeling the early-oscillatory effective axion sound speed To get a sense of the effects of the anharmonic potential on the axion fluid sound speed, we first solve the axion field perturbation equations of motion, This approximation of the fluid sound speed is shown in red in the lower subplot of Figure 2. In order to approximate the boost in the axion sound speed shown in the field equations without changing the late-time evolution of the perturbations, we modified the vanilla axion fluid sound speed to include a large negative spike just after the onset of oscillations. This negative triangular spike is shown in green in the lower subplot of Figure 2. The width and height of this spike were fit to match the approximate sound speed computed from the field perturbation solution. The width (C1) was fit to the delay in scale factor a between the onset of axion oscillations and the asymptotic sign change in the field solution sound speed. This numerical width was then approximated as a power law function of the scale factor k of the perturbation, depends linearly on the scale factor at the onset of oscillations, which in turn depends on the axion mass, fraction, and starting angle, The power spectrum results for this method can be compared to the literature, where other groups have used the exact field perturbation equations of motion to compute the matter power spectrum for extreme axions, such as Leong et al. (2019). In Figure 3 we can see the comparison in the matter power spectrum for both a vanilla axion and an extreme axion with a starting angle deviating from π by 0.2 degrees, and we find that they are in remarkably close agreement with Leong et al. (2019). However, this close agreement seems to hold best at z = 0, when these power spectra are computed, while the higher redshifts comparison may be more nuanced. Figure 2 suggests that while the exact field solution and the new approximate fluid solution agree at very late times, their evolution at early times are not fully equivalent, so more work may need to be done on this approximation in order to perform comparisons to high-redshift observables. 2.4. Using lookup tables for efficient modeling of field Extending the full field evolution so much later past the onset of oscillations requires far more computational resources than ending the field evolution as soon as oscillations begin. Greater numerical resolution, in both time and possible field potential scale, is also required to integrate these rapidly oscillating variables. With these increases to computational time, the new version of axionCAMB takes around seventy seconds to complete. While this may be feasible when computing a single power spectrum result, this is computationally intensive with which to run an MCMC analysis, which may require tens to hundreds of thousands of separate calls to axionCAMB. 2.5. Summary of changes to axionCAMB In order to model axions with extreme starting angles in a cosine field potential using the computationally efficient field formalism used in axionCAMB, we have introduced a number of modifications to axionCAMB which are explained above, but summarized here. • We replaced the quadratic approximation of the field potential with an arbitrary potential function, currently set to the canonical cosine potential. • We modified the effective axion fluid sound speed to reproduce the growth in structure seen in the exact field perturbation equations of motion. • We precomputed a lookup table for the axion background evolution which significantly reduced the runtime. The result is an accurate modeling of extreme axion background and perturbation evolution for an arbitrary axion mass, density, and starting angle that only takes ∼ 7 seconds to run. This powerful tool can shed new light on the behaviour and detectability of these extreme axion models, as discussed below. 2.6. Data: Ly-α forest estimates of the MPS [2] axionCAMB is in turn based on the cosmological Boltzmann code, CAMB (Lewis & Bridle 2002). [4] A logarithmic dependence for the background field can be derived analytically for the anharmonic corrections to the relic density (Lyth 1992).

Extreme Axions Unveiled: A Novel Fluid Approach for Cosmological Modeling - Methods

চরম অক্ষরেখা উন্মোচন: মহাজাগতিক মডেলিংয়ের জন্য একটি অভিনব তরল পদ্ধতি - পদ্ধতি

Extreme Axionen enthüllt: Ein neuartiger Fluidansatz für die kosmologische Modellierung - Methoden

Se revelan los axiones extremos: un nuevo enfoque fluido para el modelado cosmológico - Métodos

Extreme Axions dévoilés : une nouvelle approche fluide pour la modélisation cosmologique - Méthodes

चरम एक्सियंस का अनावरण: ब्रह्माण्ड संबंधी मॉडलिंग के लिए एक नवीन द्रव दृष्टिकोण - विधियाँ

極限アクシオンの解明：宇宙論モデリングのための新しい流体アプローチ - 方法

Extreme Axions 공개: 우주론적 모델링을 위한 새로운 유체 접근 방식 - 방법

Extreme Axions revelados: uma nova abordagem de fluidos para modelagem cosmológica - métodos

Представлены экстремальные аксионы: новый жидкостный подход к космологическому моделированию - Методы

Extreme Axions Ortaya Çıktı: Kozmolojik Modelleme için Yeni Bir Akışkan Yaklaşımı - Yöntemler

Ra mắt các Axion cực đoan: Một phương pháp tiếp cận chất lỏng mới cho mô hình vũ trụ - Phương pháp

揭开极端轴子的面纱：一种用于宇宙学建模的新型流体方法 - 方法

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London;
(4) DANIEL GRIN, Haverford College;
(5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro
Methods
Phenomenology
Discussion and Future Work
Conclusion
Acknowledgments and References 4. DISCUSSION AND FUTURE WORK Although comparison to LSS likelihoods from galaxy surveys, and CMB likelihoods for the lensing, temperature, and polarization power spectra are the most straightforward, the tightest current constraints on axions come from measurements of the Ly-α forest, as these are able to probe the MPS at much smaller scales than either galaxy surveys or the CMB (Rogers & Peiris 2021). However, comparing MPS predictions for extreme axions to data from the Ly-α forest is more difficult, as it requires hydrodynamical simulations of the small-scale nonlinear structure, which in principle could depend on the nonlinear behaviour of the extreme axion model. In this paper, we used the estimates of the linear MPS from the Ly-α forest data, which assumed CDM for the small-scale structure evolution, but this method is only valid in the lowaxion-density regime, where CDM makes up most of the dark matter. Some work has been done modeling the nonlinear Ly-α forest for extreme axions(Leong et al. 2019), but this simulation is computationally expensive. Ideally, the best approach would be to train an emulator to produce extreme axion predictions of the Ly-α data, similar to what was done in Rogers & Peiris (2021). When combined with our modified axionCAMB, this could allow for rapid computation and direct comparison to Ly-α forest data, which would give the most informative constraints on the small-scale behaviour of these extreme axion models. In addition, direct comparison to Ly-α observables would allow us to use higher resolution spectroscopic surveys, such as those done with Keck or VLT Lu et al. (1996); Irsiˇ c et al. ˇ (2017b). Accurate simultaneous constraints on the axion mass, density fraction, and starting angle, would quantitatively address an important question that, so far, has only been approached qualitatively: namely, the required degree of fine-tuning for these extreme axion models to work. Figure 10 shows that a good agreement with data can be reached with axion starting angles that are close to the peak, seperated by less than 10%. Arvanitaki et al. (2020) have proposed a model that could drive the axion field to start near the peak at extremely early times, but the plausibility of these models would depend on exactly how much fine tuning is required. This required degree of fine-tuning depends on the axion mass and density fraction, as seen in Figures 9, 10, and 11, and could also depend on other cosmological parameters. With our modified axionCAMB, we could create estimates of the necessary degree of fine-tuning for a range of axion and cosmological parameters, helping to inform the plausibility of these models that produce starting angles close to π. Another area worth exploring is comparing these constraints to forecast sensitivities by future CMB experiments, such as the Simons Observatory, and CMB-S4 (Hlozek et al. ˇ 2017; Lee et al. 2019; Dvorkin et al. 2022; Abazajian et al. 2022). Although Planck is already cosmic-variance limited for temperature at low-ℓ, there may be substantial improvements to be made with an experiment with better polarization and/or high-ℓ data (Aghanim et al. 2016). CMB lensing also offers the ability to probe the DM MPS at a range of scales(Rogers et al. 2023). We could also experiment with simultaneous constraints from CMB and MPS sources. Direct probes of the MPS can also be used to constrain the extreme axion model, including the Dark Energy Survey (which we used to constrain the vanilla axion model in Dentler et al. 2022), Euclid (Amendola et al. 2018), JWST (Parashari & Laha 2023), and the Vera Rubin Observatory (Mao et al. 2022). Lastly, we could try constraining potentials beyond just the standard cosine shape. Models have been proposed with axions possessing quartic, hyperbolic cosine, or monodromic potentials (Cembranos et al. 2018; Urena L ˜ opez ´ 2019;Jaeckel et al. 2017). In addition, axion-like scalar fields with a variety of potentials have been proposed as an early dark energy component potentially capable of relieving the Hubble tension (Kamionkowski & Riess 2022; Poulin et al. 2023). Axion perturbations in all of these potentials could conceivably be modeled using our modified axionCAMB, since the potential function is implemented generically. The only requirement would be that the potential being tested must simplify to a quadratic at small ϕ values, in order for the particle DM approximation to be valid at late times. This paper is available on arxiv under CC 4.0 license. Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro Methods Phenomenology Discussion and Future Work Conclusion Acknowledgments and References Abstract and Intro Abstract and Intro Methods Methods Phenomenology Phenomenology Discussion and Future Work Discussion and Future Work Conclusion Conclusion Acknowledgments and References Acknowledgments and References 4. DISCUSSION AND FUTURE WORK Although comparison to LSS likelihoods from galaxy surveys, and CMB likelihoods for the lensing, temperature, and polarization power spectra are the most straightforward, the tightest current constraints on axions come from measurements of the Ly-α forest, as these are able to probe the MPS at much smaller scales than either galaxy surveys or the CMB (Rogers & Peiris 2021). However, comparing MPS predictions for extreme axions to data from the Ly-α forest is more difficult, as it requires hydrodynamical simulations of the small-scale nonlinear structure, which in principle could depend on the nonlinear behaviour of the extreme axion model. In this paper, we used the estimates of the linear MPS from the Ly-α forest data, which assumed CDM for the small-scale structure evolution, but this method is only valid in the lowaxion-density regime, where CDM makes up most of the dark matter. Some work has been done modeling the nonlinear Ly-α forest for extreme axions(Leong et al. 2019), but this simulation is computationally expensive. Ideally, the best approach would be to train an emulator to produce extreme axion predictions of the Ly-α data, similar to what was done in Rogers & Peiris (2021). When combined with our modified axionCAMB, this could allow for rapid computation and direct comparison to Ly-α forest data, which would give the most informative constraints on the small-scale behaviour of these extreme axion models. In addition, direct comparison to Ly-α observables would allow us to use higher resolution spectroscopic surveys, such as those done with Keck or VLT Lu et al. (1996); Irsiˇ c et al. ˇ (2017b). Accurate simultaneous constraints on the axion mass, density fraction, and starting angle, would quantitatively address an important question that, so far, has only been approached qualitatively: namely, the required degree of fine-tuning for these extreme axion models to work. Figure 10 shows that a good agreement with data can be reached with axion starting angles that are close to the peak, seperated by less than 10%. Arvanitaki et al. (2020) have proposed a model that could drive the axion field to start near the peak at extremely early times, but the plausibility of these models would depend on exactly how much fine tuning is required. This required degree of fine-tuning depends on the axion mass and density fraction, as seen in Figures 9, 10, and 11, and could also depend on other cosmological parameters. With our modified axionCAMB, we could create estimates of the necessary degree of fine-tuning for a range of axion and cosmological parameters, helping to inform the plausibility of these models that produce starting angles close to π. Another area worth exploring is comparing these constraints to forecast sensitivities by future CMB experiments, such as the Simons Observatory, and CMB-S4 (Hlozek et al. ˇ 2017; Lee et al. 2019; Dvorkin et al. 2022; Abazajian et al. 2022). Although Planck is already cosmic-variance limited for temperature at low-ℓ, there may be substantial improvements to be made with an experiment with better polarization and/or high-ℓ data (Aghanim et al. 2016). CMB lensing also offers the ability to probe the DM MPS at a range of scales(Rogers et al. 2023). We could also experiment with simultaneous constraints from CMB and MPS sources. Direct probes of the MPS can also be used to constrain the extreme axion model, including the Dark Energy Survey (which we used to constrain the vanilla axion model in Dentler et al. 2022), Euclid (Amendola et al. 2018), JWST (Parashari & Laha 2023), and the Vera Rubin Observatory (Mao et al. 2022). Lastly, we could try constraining potentials beyond just the standard cosine shape. Models have been proposed with axions possessing quartic, hyperbolic cosine, or monodromic potentials (Cembranos et al. 2018; Urena L ˜ opez ´ 2019;Jaeckel et al. 2017). In addition, axion-like scalar fields with a variety of potentials have been proposed as an early dark energy component potentially capable of relieving the Hubble tension (Kamionkowski & Riess 2022; Poulin et al. 2023). Axion perturbations in all of these potentials could conceivably be modeled using our modified axionCAMB, since the potential function is implemented generically. The only requirement would be that the potential being tested must simplify to a quadratic at small ϕ values, in order for the particle DM approximation to be valid at late times.

Extreme Axions Unveiled: Discussion and Future Work

চরম অক্ষরেখা উন্মোচন: আলোচনা এবং ভবিষ্যত কাজ

Extreme Axionen enthüllt: Diskussion und zukünftige Arbeiten

Extreme Axions revelados: discusión y trabajo futuro

Extreme Axions dévoilé : discussion et travaux futurs

एक्सट्रीम एक्सियंस का अनावरण: चर्चा और भविष्य का कार्य

極限アクシオンの解明：議論と今後の取り組み

Extreme Axions 공개: 토론 및 향후 작업

Extreme Axions revelados: discussão e trabalho futuro

Представлены экстремальные аксионы: обсуждение и будущая работа

Extreme Axions Açıklandı: Tartışma ve Gelecekteki Çalışmalar

Extreme Axions được tiết lộ: Thảo luận và công việc trong tương lai

揭开极端轴子的面纱：讨论和未来工作

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London;
(4) DANIEL GRIN, Haverford College;
(5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro
Methods
Phenomenology
Discussion and Future Work
Conclusion
Acknowledgments and References 5. CONCLUSIONS Extreme axions represent an interesting class of dark matter models, possessing both interesting theoretical justifications from string theory, as well as concrete cosmological observables. Previously, their one major drawback was the high computational cost of modeling the rapid field oscillations. In this work, we have introduced a new extension to the existing axionCAMB software, allowing it to compute MPS and CMB observables for extreme axion models in ∼ 7 seconds, where previous models have taken multiple days. These observables can be computed for a range of values for the axion mass, axion DM density fraction, and extreme axion starting angle, as well as a range of ordinary cosmological parameters. We achieved this rapid modeling of the extreme axions by using a modified version of axionCAMB’s fluid approximation, reconfiguring the initial conditions to allow for finely tuned starting angles, modifying the effective fluid sound speed to reflect the tachyonic growth during the oscillatory phase, and implementing an efficient lookup table of the axion background fluid variables to allow for rapid computation. This paper is available on arxiv under CC 4.0 license. Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro Methods Phenomenology Discussion and Future Work Conclusion Acknowledgments and References Abstract and Intro Abstract and Intro Methods Methods Phenomenology Phenomenology Discussion and Future Work Discussion and Future Work Conclusion Conclusion Acknowledgments and References Acknowledgments and References 5. CONCLUSIONS Extreme axions represent an interesting class of dark matter models, possessing both interesting theoretical justifications from string theory, as well as concrete cosmological observables. Previously, their one major drawback was the high computational cost of modeling the rapid field oscillations. In this work, we have introduced a new extension to the existing axionCAMB software, allowing it to compute MPS and CMB observables for extreme axion models in ∼ 7 seconds, where previous models have taken multiple days. These observables can be computed for a range of values for the axion mass, axion DM density fraction, and extreme axion starting angle, as well as a range of ordinary cosmological parameters. We achieved this rapid modeling of the extreme axions by using a modified version of axionCAMB’s fluid approximation, reconfiguring the initial conditions to allow for finely tuned starting angles, modifying the effective fluid sound speed to reflect the tachyonic growth during the oscillatory phase, and implementing an efficient lookup table of the axion background fluid variables to allow for rapid computation.

Extreme Axions Unveiled: Conclusion

চরম অক্ষ উন্মোচন: উপসংহার

Extreme Axionen enthüllt: Fazit

Axiones extremos revelados: conclusión

Extreme Axions dévoilé : conclusion

एक्सट्रीम एक्सियंस का अनावरण: निष्कर्ष

極限アクシオンの解明：結論

Extreme Axions 공개: 결론

Extreme Axions revelados: conclusão

Представлены экстремальные аксионы: заключение

Extreme Axions Açıklandı: Sonuç

Axions cực đoan được tiết lộ: Kết luận

揭开极端轴子的面纱：结论

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto;
(3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London;
(4) DANIEL GRIN, Haverford College;
(5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro
Methods
Phenomenology
Discussion and Future Work
Conclusion
Acknowledgments and References ABSTRACT 1. INTRODUCTION Axion-like particles (ALPs) are a broad class of dark matter (DM) particle candidates that possess both a strong theoretical justification and a variety of potentially observable signatures. While the traditional quantum chromodynamics (QCD) axion is a pseudo-Nambu-Goldstone boson arising from a broken Peccei-Quinn symmetry (Peccei & Quinn 1977), ALPs can arise from broken symmetries more generally, and are produced naturally from a variety of string theories as a result of compactified higher dimensions, making them a well-motivated DM particle candidate (Dine & Fischler 1983; Preskill et al. 1983; Abbott & Sikivie 1983; Svrcek & Witten 2006; Duffy & van Bibber 2009; Arvanitaki et al. 2010; Marsh 2016; Adams et al. 2022). Throughout this work, we will use axion and ALP interchangeably to refer to this broad class of low-mass pseudo-Nambu-Goldstone boson DM candidates. Some work has been done to model the evolution of the axion field with these extreme starting angles, such as the works of Cedeno et al. ˜ (2017); Zhang & Chiueh (2017b); Leong et al. (2019); Zhang & Chiueh (2017a). However, the rapidly-oscillating nature of these axion fields (both at the background and perturbation level) necessitates extremely high temporal resolution for the computations, requiring long computation times for a brute force solution Zhang & Chiueh (2017b,a). This makes running repeated estimates of the axion evolution, of the sort required for a Markov Chain Monte Carlo (MCMC) or other likelihood sampler method, prohibitively expensive. In this work, we present a novel method of efficiently and accurately modeling the behaviour of these extreme axions as a cosmological fluid. We follow the structure of the vanilla axion modeling code axionCAMB, explained in more detail in Hlozek et al. ˇ (2015). We implement a number of innovations and improvements to axionCAMB compute predictions for cosmological observables such as the linear MPS. These innovations, described in more detail in the Section 2, include a restructuring of the initial conditions, and a novel effective sound speed of the extreme axion fluid. All of these innovations reduce the runtime to model extreme axions down to ∼ 7 seconds. This opens up new opportunities to put observational constraints on extreme axion models with higher-dimensional MCMC algorithms that require tens of thousands of calls to the axion evolution code. This paper is available on arxiv under CC 4.0 license. Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) HARRISON WINCH, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (2) RENEE´ HLOZEK, Department of Astronomy & Astrophysics, University of Toronto and Dunlap Institute for Astronomy and Astrophysics, University of Toronto; (3) DAVID J. E. MARSH, Theoretical Particle Physics and Cosmology, King’s College London; (4) DANIEL GRIN, Haverford College; (5) KEIR K. ROGERS, Dunlap Institute for Astronomy and Astrophysics, University of Toronto. Table of Links Abstract and Intro Methods Phenomenology Discussion and Future Work Conclusion Acknowledgments and References Abstract and Intro Abstract and Intro Methods Methods Phenomenology Phenomenology Discussion and Future Work Discussion and Future Work Conclusion Conclusion Acknowledgments and References Acknowledgments and References ABSTRACT 1. INTRODUCTION Axion-like particles (ALPs) are a broad class of dark matter (DM) particle candidates that possess both a strong theoretical justification and a variety of potentially observable signatures. While the traditional quantum chromodynamics (QCD) axion is a pseudo-Nambu-Goldstone boson arising from a broken Peccei-Quinn symmetry (Peccei & Quinn 1977), ALPs can arise from broken symmetries more generally, and are produced naturally from a variety of string theories as a result of compactified higher dimensions, making them a well-motivated DM particle candidate (Dine & Fischler 1983; Preskill et al. 1983; Abbott & Sikivie 1983; Svrcek & Witten 2006; Duffy & van Bibber 2009; Arvanitaki et al. 2010; Marsh 2016; Adams et al. 2022). Throughout this work, we will use axion and ALP interchangeably to refer to this broad class of low-mass pseudo-Nambu-Goldstone boson DM candidates. Some work has been done to model the evolution of the axion field with these extreme starting angles, such as the works of Cedeno et al. ˜ (2017); Zhang & Chiueh (2017b); Leong et al. (2019); Zhang & Chiueh (2017a). However, the rapidly-oscillating nature of these axion fields (both at the background and perturbation level) necessitates extremely high temporal resolution for the computations, requiring long computation times for a brute force solution Zhang & Chiueh (2017b,a). This makes running repeated estimates of the axion evolution, of the sort required for a Markov Chain Monte Carlo (MCMC) or other likelihood sampler method, prohibitively expensive. In this work, we present a novel method of efficiently and accurately modeling the behaviour of these extreme axions as a cosmological fluid. We follow the structure of the vanilla axion modeling code axionCAMB, explained in more detail in Hlozek et al. ˇ (2015). We implement a number of innovations and improvements to axionCAMB compute predictions for cosmological observables such as the linear MPS. These innovations, described in more detail in the Section 2, include a restructuring of the initial conditions, and a novel effective sound speed of the extreme axion fluid. All of these innovations reduce the runtime to model extreme axions down to ∼ 7 seconds. This opens up new opportunities to put observational constraints on extreme axion models with higher-dimensional MCMC algorithms that require tens of thousands of calls to the axion evolution code.

Extreme Axions Unveiled: A Novel Fluid Approach for Cosmological Modeling - Abstract and Intro

চরম অক্ষরেখা উন্মোচন: মহাজাগতিক মডেলিংয়ের জন্য একটি অভিনব তরল পদ্ধতি - বিমূর্ত এবং ভূমিকা

Extreme Axionen enthüllt: Ein neuartiger Fluidansatz für die kosmologische Modellierung - Zusammenfassung und Einführung

Se revelan los axiones extremos: un nuevo enfoque fluido para el modelado cosmológico: resumen e introducción

Extreme Axions dévoilé : une nouvelle approche fluide pour la modélisation cosmologique - Résumé et introduction

एक्सट्रीम एक्सियंस का अनावरण: ब्रह्माण्ड संबंधी मॉडलिंग के लिए एक नवीन द्रव दृष्टिकोण - सार और परिचय

極限アクシオンの解明: 宇宙論モデリングのための新しい流体アプローチ - 概要と序文

Extreme Axions 공개: 우주론적 모델링을 위한 새로운 유체 접근 방식 - 요약 및 소개

Extreme Axions revelados: uma nova abordagem fluida para modelagem cosmológica - Resumo e introdução

Представлены экстремальные аксионы: новый жидкостный подход к космологическому моделированию – Аннотация и введение

Extreme Axions Ortaya Çıktı: Kozmolojik Modelleme için Yeni Bir Akışkan Yaklaşımı - Özet ve Giriş

Ra mắt các trục cực mạnh: Một phương pháp tiếp cận chất lỏng mới cho mô hình vũ trụ - Tóm tắt và giới thiệu

揭秘极端轴子：一种用于宇宙学建模的新型流体方法 - 摘要和简介

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Rollover Free Accounts: How do they work?

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