Table of Links Acknowledgements 1 Introduction to thesis 1.1 History and Evidence 1.2 Facts on dark matter 1.3 Candidates to dark matter 1.4 Dark matter detection 1.5 Outline of the thesis 2 Dark matter through ALP portal and 2.1 Introduction 2.2 Model 2.3 Existing constraints on ALP parameter space 2.4 Dark matter analysis 2.5 Summary 3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction 3.2 Model 3.3 Theoretical and experimental constraints 3.4 Phenomenology of dark matter 3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻 3.6 Summary 4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction 4.2 Model 4.3 Theoretical and experimental constraints 4.4 Dark Matter analysis 4.5 Summary 5 Summary Appendices A Standard model B Friedmann equations C Type I seasaw mechanism D Feynman diagrams in two-component DM model Bibliography 1.1 History and Evidence In 1884, Lord Kelvin estimated the number of dark bodies in the Milky Way from the observed velocity dispersion of the stars orbiting around the center of the galaxy. By using these measurements, he estimated the mass of the galaxy, which he determined to be different from the mass of visible stars. He thus concluded that many of our stars, perhaps a great majority of them, maybe dark bodies [40]. In 1906, Henri Poincare, in "The Milky Way and Theory of Gases," used "dark matter" or “matière obscure” in French in discussing Kelvin’s work [3]. In 1930, J.H. Oort studied the Doppler shift of the stars moving near the galactic plane of the Milky Way, and from that, he calculated the velocities of stars. He found that stars are moving sufficiently fast that they can escape the gravitational pull of the luminous mass of the galaxy, calculated by the mass (M)/luminosity (L) ratio method, which implies that there must be an invisible gravity source that holds stars in the galactic plane [41]. In 1933, F. Zwicky studied the Coma cluster, which is about 99 Mpc away from Earth. He calculated the velocity dispersion of the galaxies using Doppler shift data and applying the Virial theorem, and he found that the total mass of the cluster is just 2% of the one calculated by the M/L ratio method, leading to the conclusion of invisible mass, which he called "Dunkle Materie" or dark matter [42]. In 1960–1970, Vera Rubin, with others [43], studied the rotation curves of sixty isolated galaxies, from which she estimated the rotation velocities of the region of a galaxy using Doppler shift and found that it is independent of distance, as shown in figure 1.1. Assuming Newtonian gravity and circular orbits, the velocity of the star is given by The phenomenon of gravitational lensing, described by General Relativity (GR), states that whenever light from a distant source passes near a massive object, it forms a ring of light called “Einstein ring" around the same object. In 1979, D. Walsh was the first to study two distant objects separated by only 5.6 arcseconds with very similar redshifts. The explanation for his discovery is that there was only one object there, and the other is the image of it formed by an unseen dark matter cloud [44]. In 2004, from Chandra’s observations of the bullet cluster (1E0657–56), Markevitch and Clowe found the most compelling reason for the presence of the invisible matter. A bullet cluster is a system of two colliding galactic clusters. During the collision, the galaxies, which are separated by large distances within the two clusters, pass right through without interacting. However, the majority of the cluster’s baryonic mass exists in the hot gas in between galaxies. Collision dislocates the stellar gasses from their respective galaxies and heats the gases, resulting in a huge amount of X-ray radiation emission. However, the location of baryonic mass (stellar gases) seen by an X-ray telescope is different from the one found by weak gravitational lensing, i.e., the region of space where most masses are located, as shown in figure 1.2. If an unseen mass is electromagnetically neutral, then during a collision, it won’t be dragged and will remain in its separate clusters, which explains this puzzle [2]. In 1964, two American radio astronomers, Arno Penzias, and Robert Wilson, accidentally discovered the earliest radiation (uniform radio waves) or so-called cosmic microwave background radiation (CMBR) in the universe. Later in 1989, the COBE satellite confirmed this extreme uniform relic radiation at 2.73 K, with tiny spatial fluctuations in temperature. In 2001, WMAP and later Planck confirmed the prediction of COBE, measured the temperature fluctuation with greater accuracy, and found that it was of the order of 𝜇K. This whole observation was done via the power spectrum method, which is shown in figure 1.3. It has been found that these temperature fluctuations in the early universe can be explained only if one accounts for the additional non-baryonic matter, which is nearly five times ordinary matter [45]. This paper is available on arxiv under CC BY 4.0 DEED license. Author:
(1) Shivam Gola, The Institute of Mathematical Sciences, Chennai. Table of Links Acknowledgements Acknowledgements 1 Introduction to thesis 1 Introduction to thesis 1.1 History and Evidence 1.1 History and Evidence 1.2 Facts on dark matter 1.2 Facts on dark matter 1.3 Candidates to dark matter 1.3 Candidates to dark matter 1.4 Dark matter detection 1.4 Dark matter detection 1.5 Outline of the thesis 1.5 Outline of the thesis 2 Dark matter through ALP portal and 2.1 Introduction 2 Dark matter through ALP portal and 2.1 Introduction 2.2 Model 2.2 Model 2.3 Existing constraints on ALP parameter space 2.3 Existing constraints on ALP parameter space 2.4 Dark matter analysis 2.4 Dark matter analysis 2.5 Summary 2.5 Summary 3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction 3 A two component dark matter model in a generic 𝑈(1)𝑋 extension of SM and 3.1 Introduction 3.2 Model 3.2 Model 3.3 Theoretical and experimental constraints 3.3 Theoretical and experimental constraints 3.4 Phenomenology of dark matter 3.4 Phenomenology of dark matter 3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻 3.5 Relic density dependence on 𝑈(1)𝑋 charge 𝑥𝐻 3.6 Summary 3.6 Summary 4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction 4 A pseudo-scalar dark matter case in 𝑈(1)𝑋 extension of SM and 4.1 Introduction 4.2 Model 4.2 Model 4.3 Theoretical and experimental constraints 4.3 Theoretical and experimental constraints 4.4 Dark Matter analysis 4.4 Dark Matter analysis 4.5 Summary 4.5 Summary 5 Summary 5 Summary Appendices Appendices A Standard model A Standard model B Friedmann equations B Friedmann equations C Type I seasaw mechanism C Type I seasaw mechanism D Feynman diagrams in two-component DM model D Feynman diagrams in two-component DM model Bibliography Bibliography 1.1 History and Evidence In 1884, Lord Kelvin estimated the number of dark bodies in the Milky Way from the observed velocity dispersion of the stars orbiting around the center of the galaxy. By using these measurements, he estimated the mass of the galaxy, which he determined to be different from the mass of visible stars. He thus concluded that many of our stars, perhaps a great majority of them, maybe dark bodies [40]. In 1906, Henri Poincare, in "The Milky Way and Theory of Gases," used "dark matter" or “matière obscure” in French in discussing Kelvin’s work [3]. In 1930, J.H. Oort studied the Doppler shift of the stars moving near the galactic plane of the Milky Way, and from that, he calculated the velocities of stars. He found that stars are moving sufficiently fast that they can escape the gravitational pull of the luminous mass of the galaxy, calculated by the mass (M)/luminosity (L) ratio method, which implies that there must be an invisible gravity source that holds stars in the galactic plane [41]. In 1933, F. Zwicky studied the Coma cluster, which is about 99 Mpc away from Earth. He calculated the velocity dispersion of the galaxies using Doppler shift data and applying the Virial theorem, and he found that the total mass of the cluster is just 2% of the one calculated by the M/L ratio method, leading to the conclusion of invisible mass, which he called "Dunkle Materie" or dark matter [42]. In 1960–1970, Vera Rubin, with others [43], studied the rotation curves of sixty isolated galaxies, from which she estimated the rotation velocities of the region of a galaxy using Doppler shift and found that it is independent of distance, as shown in figure 1.1. Assuming Newtonian gravity and circular orbits, the velocity of the star is given by The phenomenon of gravitational lensing, described by General Relativity (GR), states that whenever light from a distant source passes near a massive object, it forms a ring of light called “Einstein ring" around the same object. In 1979, D. Walsh was the first to study two distant objects separated by only 5.6 arcseconds with very similar redshifts. The explanation for his discovery is that there was only one object there, and the other is the image of it formed by an unseen dark matter cloud [44]. In 2004, from Chandra’s observations of the bullet cluster (1E0657–56), Markevitch and Clowe found the most compelling reason for the presence of the invisible matter. A bullet cluster is a system of two colliding galactic clusters. During the collision, the galaxies, which are separated by large distances within the two clusters, pass right through without interacting. However, the majority of the cluster’s baryonic mass exists in the hot gas in between galaxies. Collision dislocates the stellar gasses from their respective galaxies and heats the gases, resulting in a huge amount of X-ray radiation emission. However, the location of baryonic mass (stellar gases) seen by an X-ray telescope is different from the one found by weak gravitational lensing, i.e., the region of space where most masses are located, as shown in figure 1.2. If an unseen mass is electromagnetically neutral, then during a collision, it won’t be dragged and will remain in its separate clusters, which explains this puzzle [2]. In 1964, two American radio astronomers, Arno Penzias, and Robert Wilson, accidentally discovered the earliest radiation (uniform radio waves) or so-called cosmic microwave background radiation (CMBR) in the universe. Later in 1989, the COBE satellite confirmed this extreme uniform relic radiation at 2.73 K, with tiny spatial fluctuations in temperature. In 2001, WMAP and later Planck confirmed the prediction of COBE, measured the temperature fluctuation with greater accuracy, and found that it was of the order of 𝜇K. This whole observation was done via the power spectrum method, which is shown in figure 1.3. It has been found that these temperature fluctuations in the early universe can be explained only if one accounts for the additional non-baryonic matter, which is nearly five times ordinary matter [45]. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv Author: (1) Shivam Gola, The Institute of Mathematical Sciences, Chennai. Author: Author: (1) Shivam Gola, The Institute of Mathematical Sciences, Chennai.

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