Probing early universe with primordial relics from inflation: primordial blackholes, dark matter and dark radiation тема диссертации и автореферата по ВАК РФ 01.04.02, кандидат наук Порей Шиладитья

• Порей Шиладитья
• кандидат наук
• 2024

Оглавление диссертации кандидат наук Порей Шиладитья

Contents

1 Introduction

1.1 Relevance of the topic

1.2 The purpose of the work

1.3 Theoretical and practical significance

1.4 Scientific novelty

1.5 Approbation of results

1.6 Structure of the thesis

2 Brief overview of ACDM cosmology

2.1 Metric and Hubble parameter

2.2 Einstein equation and energy-momentum tensor

2.3 Thermal history of the universe

2.4 Conservation of entropy

2.5 Neutrino Decoupling

2.6 BBN

2.7 Recombination

2.8 Shortcomings of standard model of cosmology

2.8.1 Flatness problem

2.8.2 Horizon problem

2.8.3 Slow roll inflation

2.9 Perturbation

2.10 Dark matter

3 Chapter PBH

3.1 Introduction

3.2 Dolgov-Silk mechanism of PBH formation

3.3 Log-normal mass spectrum

3.4 Fixing parameters from the present-day observed data

3.4.1 Mass spectrum of black holes in the galaxy

3.4.2 Total mass density of black holes

3.4.3 Supermassive PBHs in the center of large galaxies

3.4.4 Estimation of parameters and number density of Intermediate mass black holes

3.5 GW from the coalition of PBH-pairs

3.5.1 Chirp Mass and cumulative distribution of Chirp Mass

3.5.2 Statistical analysis and result

3.6 Discussion

3.6.1 Low spin of BHs : PBHs vs astrophysical models

3.6.2 MACHO

4 Inflation and BSM particles as DM

4.1 Inflection-point Inflation Models

4.1.1 Inflection-point achieved with Linear term

4.1.2 Inflection-point achieved with Sextic Term

4.2 Stability analysis

4.2.1 Stability analysis for linear term inflation

4.2.2 Stability analysis for sextic inflation

4.3 Reheating and Dark Matter

4.4 Production of Dark Matter and Relic Density

5 Measuring inflaton couplings with dark radiation as Neff in CMB

5.1 Effective number of relativistic degrees of freedom

5.2 Inflation and Dark Radiation

5.2.1 Hilltop Inflation (H-I)

5.2.2 Natural Inflation (N-I)

5.2.3 Coleman-Weinberg Inflation (C-I)

5.2.4 Starobinsky Inflation (S-I)

5.3 Inflaton decay during reheating

5.4 Inflaton Decaying to Dark Radiation

5.4.1 Reheat temperature

6 Summary, conclusions and future directions

6.1 The main provisions for the defense:

6.2 Major outcomes of the thesis

6.2.1 Log-normal mass spectrum of PBHs

6.2.2 BSM particles as non-thermal DM, and slow roll inflation

6.2.3 BSM particles as DR, and slow roll inflation

6.3 Future directions

A Appendix

A.1 Estimation of number density of IMBHs

A.2 Constraints on /pbh for different mass range of PBHs(M denotes that mass of PBH)

B Appendix

B.1 Planck2018+BICEP3+Keck Array2015 bound on ns - r plane

B.2 Generalized version of Hilltop inflation and Coleman-Weinberg inflation for

/cw >mp

B.3 Contribution in ANeff for scalar DR produced from 00 ^ cp^

B.4 range of couplings such that BSM particles can not reach in thermal equilibrium with SM plasma

List of Figures

2.1 AT as a function of

3.1 The parameters of the black-hole-distribution in galaxies assuming it follows Gaussian function, best-fit by a narrow distribution with peak at

7.8 ± 1.2M© [204]

3.2 Model distribution FPBH(< M) with parameters M0 and Ypbh (in this figure y = Ypbh) for two best Kolmogorov-Smirnov tests. EDF= empirical distribution function

3.3 Model distribution FPBH(< M) with parameters M0 and Ypbh (in this figure y = Ypbh) for two best Van der Waerden tests. EDF= empirical distribution function

3.4 Cumulative distributions FABH(< M) for two astrophysical models of BH-BH coalescences - C-O core collapse and CE

3.5 Gravitational lensing constraints for MACHOs

4.1 Top-left panel: Normalized U$($) (Eq. (4.22)) as a function $/MP for benchmark value from Table

4.2 Top-left panel: Normalized Uip(p) (Sec. 4.1.2) as a function of p/MP for benchmark value from Table

4.3 Illustration of permissible upper limits for yx and A12 obtained from stability analysis in Model I SRI

4.4 Illustration of permissible upper limits for yx and A12 obtained from stability analysis in Model II SRI

4.5 Variation of Tmax/Trh as a function of Trh: left panel is for the linear term SRI, whereas right panel is for the sextic term SRI. The apple green-shaded stripe presents lower bound on Trh i.e. Trh ^ 4MeV, and higher bound on Trh are demonstrated by the blue-shaded region. The upper bound arises from the stability analysis (see Eq. (4.40) andEq. (4.47))

4.6 The allowed region (unshaded) for the Yukawa-like coupling yx to produce the entire CDM of the present universe: left panel is for Model I inflation and right for Model II inflation

4.7 mxxYield of DM produced from the 2-to-2 scattering with graviton as mediator for different values of mx

5.1 This figure displays ns — r predictions for four inflationary models: H-I, N-I, C-I, and S-I, as well as 1 — o and 2 — o best fit contour when Neff is fixed at SM value and when it is treated as free variable

5.2 This figure illustrates ANeff as a function of BX from Eq. (5.26)

5.3 This figure presents 1 — o and 2 — o best-fit contours from [369], and predicted ranges of r of the four aforementioned slow roll inflationary models on (r, BX) plane

5.4 Colored lines outline parameter space on the plane of couplings within current bounds ANeff obtained from observed data of CMB and future prospective reaches for upcoming CMB observations mentioned in Table

5.5 This figure illustrates how the permissible parameter space (or the parameter space that is within the reach of sensitivity of upcoming CMB observations) on (A^X, \\2,H) plane changes when o'm, Am are varied from

m^

5.6 In this figure, inclined lines correspond to fixed values of A^X, while horizontal lines denote present bounds and prospective future reaches on ANeff for forthcoming CMB observations listed in Table 5.1, on (ANeff, Ai2,h ) plane

B.1 This figure displays ns — r predictions for four inflationary models : HI, N-I, C-I, and S-I, alongside current 1 — a and 2 — a best fit contour when ANeff = 0 from Planck2018 (in green shading), Planck2018+BICEP3+Keck Array2018 (in yellow shading), and forthcoming CMB observation (SO)

represented by the black shaded region

B.2 Left panel: Presenting predicted values of ns — r for regularized Hilltop inflation ( Eq. (B.1)) and C-I inflationary model ( Eq. (5.9)) for few ^ MP alongside 1 — a and 2 — a best-fit contour from Planck2015, and Planck2015+BICEP2-Keck Array2015, and bound derived from analysis

considering Neff as a variable [24, 348], as detailed in Fig

B.3 Variation of ANeff versus r\ for three different values of y^hh/H (in this figure y = Y^hh) for a scalar BSM particle (<) contributing to ANeff and

produced via Eq. (5.34)

B.4 In order for DR particles to remain out of thermal equilibrium with the SM Higgs through the inflaton exchange processes at the tree level, representative sets of values for the couplings (A12,H, A12,^) (top-right panel), (A12,h,yx) (top-left panel), (A12,H, g^Y) (bottom panel) are shown

List of Tables

1 Common acronyms used throughout this thesis

2.1 Values of some of the ЛСБМ parameters from CMB (hCM в ~ 0.674)

2.2 Constraints on As, ns, and r

4.1 Benchmark value for иФ from Eq. (4.22), with ФШт indicating the minimum of potential

4.2 Benchmark values for sextic potential (фШт is the minimum of potential

Eq. (4.31))

5.1 Bounds on Neff (or Д Neff )from observed data from CMB, and prospective future reaches of Neff (or Д^д) that upcoming CMB experiments may be able to observe [332, 333]

5.2 Benchmark value for four inflationary models mentioned in Secs

to 5.2.4 (ln(l010As) = 3.047, see Table 2.2)

5.3 For benchmark value from Table 5.2, estimation of Trh and NRH for different interaction Eqs. (5.30), (5.32) and (5.33), and for four inflationary model Secs. 5.2.1 to

A.1 Estimation of number density of intermediate mass black holes (N1MBH). Here is the value of ^ estimated from the condition Nga1 = 0.1/Mpc3 (see Sec. 3.4.3), and is the value of ^ estimated from the condition PPBH = fpbh 2.5 10-30 g/cm3 (see Eqs. (3.6) and (3.7)). Mo, Ypbh, and ^ are three parameters of log-normal mass function defined in Eq. (3.5). Mmax and Mb are defined in Eqs. (3.6) and (3.8), respectively. M1MBH represents the mass of IMBH, while M1MBH denotes the number density of IMBHs per galaxy

A.2 Constraints on fpbh for different mass range of PBHs

Введение диссертации (часть автореферата) на тему «Probing early universe with primordial relics from inflation: primordial blackholes, dark matter and dark radiation»

Introduction

1.1 Relevance of the topic

The ACDM (Lambda Cold Dark Matter) cosmological model continues to maintain its position as the most successful framework in cosmology, even after the publication of data from the Planck 2018 mission [2, 3]. This is due to the fact that this model is exceptionally successful in theoretically predicting observed data. Beside its ability to describe the expansion of the universe from a high-energy state, the ACDM model excels in two specific predictions: the Cosmic Microwave Background (CMB) and Big Bang Nucleosynthesis (BBN). The Planck satellite has provided the most precise data to date of the power spectrum of CMB temperature and polarization anisotropy using six primary cosmological parameters. Along with this, data from other independent CMB observations, including from ground-based CMB experiments, such as Atacama Cosmology Telescope (ACT) [4, 5], the South Pole Telescope (SPT) collaborations [6, 7] etc. is consistent with the flat ACDM universe characterized by a power-law primordial spectrum, offering compelling support for the theory of cosmic inflation.

Currently, BBN which happens when temperature of the universe is ~ 1.8 MeV [8], is the earliest cosmic epoch whose microphysics is well understood and the theoretical predictions about the weighted average deuterium abundance relative to proton [9], and helium-4 (4He) of this era agrees remarkably well with observed data [10]. The underlying theory of production of light elements during BBN era relies mainly on the standard model of particle physics (SM), and general theory of relativity. It also depends on the baryon-to-photon ratio, and effective number of neutrinos. Nonetheless, the cosmic epochs that precede this era remain less clearly understood. Before this era, two important phase transitions are believed to have happened, but we do not have complete knowledge about the dynamics of those phase transitions. The first one involves breaking of global chiral sym-

metry and is called as the QCD (quantum chromodynamics) phase transition. The second phase transition happens when the Higgs boson gains non-zero vacuum expectation value and electroweak gauge symmetry breaks. To investigate further back along the timeline of the universe, we must consider beyond the Standard Model (BSM) to address the many questions raised by observed data. BSM physics, which has minimal interactions with SM, remains largely unexplored through laboratory experiments. Therefore, it remains plausible that new physics played a pivotal role in the early universe before the era of BBN. For instance, in the early universe, matter and antimatter were expected to exist in equal quantities, but the present observable universe shows absence of antimatter in significant amount. Unfortunately, we can not look further back in time using CMB photons due to their opacity in the pre-recombination plasma - due to Thomson scattering of photons they lose the information. Nevertheless, the early universe has left behind primordial relics, including Gravitational Wave (GW) [11], Primordial Black Holes (PBHs) [12-16] and relics of BSM particles, whether massive or light. If these BSM particles were unstable, they could have decayed, contributing, for example, to the generation of the observed baryon asymmetry [17-20]. If they are stable, they may have contributed to Cold Dark Matter (if massive) [21, 22] or to the effective number of relativistic species [23-25] (if light) of the present universe. In this work we focus on the latter category of relics.

The origin of small primordial fluctuations in the early universe, which are responsible for generating both the small anisotropy in the background of the CMB and large-scale structures (LSS) like galaxies, can be explained if there was an inflationary epoch in the very early universe. During cosmic inflation, the Hubble parameter is nearly constant, which implies quasi de-sitter universe, but cosmological scale factor increases exponentially. Consequently, scale invariant quantum fluctuation generated during cosmic inflation may leave the Hubble horizon and may reenter at later universe to generate large scale structure, or even maybe PBHs. This epoch washes out primordial anisotropies, if was present before this cosmological inflation, in energy-momentum tensor and specetime metric. Due to this reason, resulting in flat universe with CMB photons with present day uniform blackbody temperature of ~ 2.725 K. Since its first proposing in Refs. [26-29], a number of inflationary models have been proposed. however, simplest model of chaotic inflation with potential of inflaton ^ is given by Va with p > 1, are not supported by recent Planck+BICEP data [30, 31]. However, plateau like potential are favoured for slow roll inflation (SRI), and there are two possible ways to obtain such potential: SRI near

inflection point and inflationary scenario where inflaton is non-minimally coupled gravity (Ricci scalar) (for example, see Refs. [32, 33]).

In addition to that, Planck data shows that ~ 26.5% of total matter-energy density of the universe is in the form of dark matter (DM). However, true nature of DM is still not known with certainty. The problem becomes extremely challenging because DM interacts with other baryonic matters only via gravitational interaction and does not emit, absorb or reflect light at all. Despite these, scientists have managed to collect many observed-evidences about the presence of DM. Nowadays, we are familiar with the fact that each galaxy posses its own DM halo, including our own Milky Way. We are here interested in only those DM whose free-streaming length is shorter in comparison to proto-galaxy (so that they are capable of forming the galactic structure) i.e. Cold Dark Matter (CDM). The presence of CDM provides the proper explanation for the extra non-luminous mass of galaxies in their halo, their rotation curves, and the collision of bullet clusters [34], or gravitational lensing of the foreground galaxies.

In spite of all these efforts, it is impossible today to claim with certainty what are the constituents of the DM halo as there is still no unequivocal theory about them. Two of the popular proposed viable candidates for DM are PBHs and Massive Astrophysical Compact Halo Objects, also known as MACHOs. PBHs formed long before the first star in the universe appeared. Since the initial proposal [35-38] regarding their existence, numerous mechanisms have been suggested for their formation. These mechanisms include direct collapse from quantum fluctuations generated during cosmic inflation (for example, see Refs. [39-41]), as well as collapse and fragmentation [42] of high-energy scalar fields resulting from bubble collisions, due to gravitational instability of scalar fields [43], and the collapse of Domain Walls due to first and second-order phase transitions [44]. Theoretically, it is possible that PBHs can be found in a really wide mass range [45] (from a fraction of solar mass (10-18M0) to billion times solar mass). Hence, to estimate the contribution of PBH within a particular mass range to CDM, mass function of PBH is necessary. A simple assumption for the mass function is that all the PBHs produced from collapse have the same mass. For other extended mass functions of PBHs, see Refs. [4652]. In our work, we consider PBHs which are formed via the mechanism described in Refs. [1, 53]. The mass function of PBHs formed through that mechanism have lognormal mas function at their time of formation. Historically, this is the first mass function of PBHs that was proposed based on rigorous mathematical calculations.

It is probably less probable that PBHs cotribute 100% of the total CDM density (see Refs. [12, 15, 54-56]). Then, alternate possibility is is mixed DM scenario (such as PBH+BSM DM particles) [57, 58]. However, to fully understand this scenario, including whether both DM components are compatible with each other, we need to know the exact nature of both DM components (see Ref. [59]). In this work, we consider the simplest scenario in which 100% of total CDM is contributed by a single type of BSM particle. Non-baryonic particles present in some extension of the SM; including multi-charged stable particles, dark atoms, mirror matter, WIMP, SIMP, Axion, LSP, etc [60] have been proposed as viable candidate for DM particles. Particle DM can be categorized into two groups based on the mechanism of their evolution. Initially at very high temperature, thermal DM particles were in thermal equilibrium with the plasma of relativistic SM particles. As the temperature drops to the order of mass of the DM particles (an also depends of the coupling between DM particle and SM particles), the number density of DM particles starts to decrease exponentially. This continues until the decay with of those particles becomes < H, where H represents the Hubble parameter. Afterward, the comoving number density of dark matter particles remains constant. This mechanism is called freeze out, with thermal WIMPs [61] being a well-known example. Although, thermal DM is expected to be detectable through particle detectors, indirect detection, or cosmic rays, no signatures confirming its existence have been obtained so far [62-65]. In that context, non-thermal DM scenario appears more plausible. In this scenario, DM particles are produced either through the decay of massive particles or via interactions with SM plasma of the universe. As long as this reaction rate > H, production of DM particle continues, but these particles never reach thermal equilibrium with the SM plasma. Hence, these particles are called Feebly Interacting Massive Particles (FIMPs). The mechanism of particle production in this case is called Freeze-in. In this work, we consider the DM particles are non-thermal, and the BSM particles contributing to the DM sector are produced from the decay of the inflaton. We aim to develop a unified model that integrates both inflation and the generation of dark matter. Inflaton as a singlet to SM gauge group has been explored in Refs. [66, 67]. Specifically, the incorporating a non-minimal coupling between the inflaton and the Ricci scalar, as discussed in Refs. [68-79], leads to the generate more flat potential in the Einstein frame. Flat potentials, devoid of such non-minimal gravitational coupling, have also been considered in BSM scenarios, such as SMART U(1)X [80], the NMSM [81], WIMPflation [82], the vMSM [83], models featuring a single axion-like particle [84], and extensions incorporating a complex flavon field [85]. Fur-

thermore, Ref. [86] has dicussed the possibility of detecting GW signature for the inflaton decay as a potential source of dark matter. Inflection-point inflation is very popular in the literature as it can easily create flat-potential for slow roll inflation within various particle physics models, particularly in the context of BSM theories [87-106]. It effectively addresses trans-Planckian issues [107] and agrres well with the swampland distance conjecture [108] by employing a small-field inflation scenario. Furthermore, it often leads to a testable running of the spectral index (as ~ 0(10-3)) in foreseeable future observations [109]. Additionally, inflection-point inflation can result in a notably low inflation scale (HI), thus resolving cosmological moduli issues in the universe [110].

At the end of a slow-roll inflationary phase, the universe finds itself at an extremely low temperature state. The post-inflationary reheating era serves as the bridge between the inflaton-dominated early universe and the hot universe that we observe today. During this reheating epoch, the inflaton field typically undergoes oscillations around the minimum of its potential energy, leading to the transfer of its energy into the generation of both SM particles and BSM particles through various interactions, including gravitational ones. As a result, this highly adiabatic epoch leads to a significant increase in the temperature of the universe. These BSM particles can potentially contribute to the dark matter sector or remain relativistic, contributing as dark radiation (DR). DR, in turn, can influence the expansion rate of the universe, the measured value of Hubble parameter, CMB anisotropy [111], and the perturbations responsible for large-scale structure formation [112]. Furthermore, DR can arise from the decays of massive particles [113] or from U(1) gauge fields that are singlets under the SM [114]. Several particle candidates, including light sterile neutrinos [115, 116], Goldstone bosons [23], neutralinos [117], axions [118, 119], and early dark energy [120], have been proposed as viable contributors to the category of DR.

1.2 The purpose of the work

The purpose of this thesis is to investigate relic densities generated by cosmic inflation, focusing on CDM and relativistic free-streaming particles known as Dark Radiation (DR). The objectives are as follows:

• To estimate the parameters of the log-normal mass function of PBHs, assuming the

possibility of the CDM being entirely or partially composed of PBHs with a mass function that follows a log-normal distribution. Those PBHs are produced due to coupling between inflaton and a complex BSM field.

• To explore the permissible parameter space of the coupling (yx) of a non-thermal fermionic BSM particle x with the inflaton, and the mass (mx) of the x particle, considering the scenario where CDM is entirely comprised of such particles produced from the decay of the inflaton.

• To investigate the scenario where an additional relativistic non-thermal BSM particle is produced solely from the decay of the inflaton, contributs to ANeff, and to explore how bounds on ANeff can constrain the permissible parameter space of the couplings with the inflaton.

This work also opens up a possible window for probing into the early universe, particularly the era of cosmic inflation, and its role in generating CDM density and DR.

1.3 Theoretical and practical significance

By using the estimated values of the parameters of log-normal mass spectrum, we calculated the number density of intermediate mass black holes (IMBHs). IMBHs are expected to be PBHs, and act as progenitor for the formation of galaxies. The future detection of more IMBHs can lend support to the notion and may also serve to validate our calculations. The permissible range of the coupling of DM particle x with inflaton, yx, and mass of x particles, mx, that we found depends on benchmark values as well as inflationary models. The benchmark we chose for slow roll inflation can be tested by forthcoming CMB observations with higher sensitivity. Since inflation is the only source of primordial B-mode polarization, detection of B-mode polarization by future GW detectors can provide conclusive evidence of cosmic inflation. Those CMB and GW observations can also provide more stringent bounds on ANeff.

1.4 Scientific novelty

Log-normal mass function of PBHs is historically the first mass function based on rig-

orous mathematical calculations. We estimated the parameters of the log-normal mass function based on new set of observed data, including GW data from LIGO/VIRGO. We consider near inflection point slow roll inflation for two models of potential and find benchmark values satisfying current CMB constraints and consequently the range of yx and mx. We are one of the first groups that propose the production of relativistic BSM particles from the decay of inflaton and put constraints on the branching fraction from the Planck data.

1.5 Approbation of results

The main results of the thesis were repeatedly reported and discussed at scientific seminars at the Novosibirsk State University (including 'Seminar organized by Professor Boris Albertovich Schwartz) and at the following three international conferences and schools: Moscow International School of Physics (MISP) (Moscow, Russia, 2019), 6th International Conference on Particle Physics and Astrophysics (ICPPA-2022) - Moscow, Russia (conference proceeding: 1), and XXV Bled Workshop-"What comes beyond the Standard Model?" (Bled, SLovenia, 2022) (conference proceeding: 2). Parts of this thesis have been presented to the scientific community at various research institutions, including the Indian Association for the Cultivation of Science (IACS) on February 12, 2024, the Physics & Applied Mathematics Unit (PAMU) at the Indian Statistical Institute, the Saha Institute of Nuclear Physics1 (SINP), the Ramakrishna Mission Vivekananda Educational and Research Institute, the Indian Institute of Science Education and Research (IISER) in Berhampur, the Indian Institute of Technology in Kharagpur (IIT KGP), the Centre for High Energy Physics (CHEP) at the Indian Institute of Science in Bengaluru (IISc), the Raman Research Institute2 (RRI), and the Indian Institute of Astrophysics (IIA) in Bengaluru.

Based on the materials of the dissertation, 4 scientific works (1 - 4) were published in international peer-reviewed journals included in the "highest attestation committee" list.

1Details: https://www.saha.ac.in/web/theory-recent-colloquia1?cq_id=683

2Details: https:/ /www. rri.res.in/ events/primordial- relics- inflation-dar k-matter-dark-radiation-and-baryon-asymmetry

1.6 Structure of the thesis

This thesis is organised as follows: In Chapter 2, we briefly discuss relevant formulas in ACDM cosmology. In Chapter 3, we estimate the parameters of log-normal mass function for PBHsfrom the available observed data, as well as with the assumption that the BH binaries whose merging events has been detected by GW detector LIGO-VIRGO in O1-O3 runs. In Chapter 4, we consider inflection point inflation and production of gauge singlet fermion field x as the non-thermal DM candidate during reheating era. In Chapter 5, we consider production of a relativistic BSM particle as DR, and its impact on the selection for viable model for slow roll inflation and couplings with inflaton using data available from CMB observations. In Chapter 6, we discuss the summary and conclusions.

2

Brief overview of ACDM cosmology

The Big Bang theoretical model of cosmology describes the origin of the expanding universe from a very hot and very dense state. The ACDM model of the universe, often referred as concordance model [121] of cosmology, is an extension of Big Bang model of the universe, which incorporates CDM [122] and dark energy [123]: A in ACDM denotes dark energy while CDM represents cold dark matter [124]. This cosmological model mainly relies on six cosmological parameters [125, 126]: the cold dark matter density, the reduced Hubble parameter, the baryon density, the optical depth to reionization, and As (amplitude of scalar power spectrum) and ns (scalar spectral index) [127], and matches remarkably well with the observed data, earning it the designation as the standard model of cosmology. In this chapter, we briefly review the mathematical formulas of ACDM model that are relevant in the subsequent sections.

Список литературы диссертационного исследования кандидат наук Порей Шиладитья, 2024 год

Bibliography

[1] A. Dolgov and J. Silk, Phys. Rev. D 47, 4244 (1993).

[2] N. Aghanim et al. (Planck), Astron. Astrophys. 641, A6 (2020), [Erratum: As-tron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO] .

[3] N. Aghanim etal. (Planck), Astron. Astrophys. 641, A5 (2020), arXiv:1907.12875 [astro-ph.CO] .

[4] S. Aiola et al. (ACT), JCAP 12, 047 (2020), arXiv:2007.07288 [astro-ph.CO] .

[5] S. K. Choi et al. (ACT), JCAP 12, 045 (2020), arXiv:2007.07289 [astro-ph.CO] .

[6] D. Dutcher et al. (SPT-3G), Phys. Rev. D 104, 022003 (2021), arXiv:2101.01684 [astro-ph.CO] .

[7] L. Balkenhol et al. (SPT-3G), Phys. Rev. D 108, 023510 (2023), arXiv:2212.05642 [astro-ph.CO] .

[8] K. N. Abazajian and H. G. Escudero, (2023), arXiv:2309.11492 [hep-ph] .

[9] S. Riemer-S0rensen and E. S. Jenssen, Universe 3, 44 (2017), arXiv:1705.03653 [astro-ph.CO] .

[10] C. A. Bertulani, F. W. Hall, and B. I. Santoyo, EPJ Web Conf. 275, 01003 (2023), arXiv:2210.04071 [nucl-th] .

[11] L. Krauss, S. Dodelson, and S. Meyer, Science 328, 989 (2010), arXiv:1004.2504 [astro-ph.CO] .

[12] B. Carr, S. Clesse, J. Garcia-Bellido, M. Hawkins, and F. Kuhnel, (2023), arXiv:2306.03903 [astro-ph.CO] .

[13] B. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, Rept. Prog. Phys. 84, 116902 (2021), arXiv:2002.12778 [astro-ph.CO] .

[14] A. Escriva, F. Kuhnel, and Y. Tada, (2022), arXiv:2211.05767 [astro-ph.CO] .

[15] B. Carr and F. Kuhnel, Ann. Rev. Nucl. Part. Sci. 70, 355 (2020), arXiv:2006.02838 [astro-ph.CO] .

[16] M. Y. Khlopov, Res. Astron. Astrophys. 10, 495 (2010), arXiv:0801.0116 [astro-ph] .

[17] T. Asaka, K. Hamaguchi, M. Kawasaki, and T. Yanagida, Phys. Rev. D 61, 083512 (2000), arXiv:hep-ph/9907559 .

[18] A. Kusenko, K. Schmitz, and T. T. Yanagida, Phys. Rev. Lett. 115, 011302 (2015), arXiv:1412.2043 [hep-ph] .

[19] M. Fukugita and T. Yanagida, Phys. Lett. B 174, 45 (1986).

[20] A. D. Dolgov, in 163rd Course of International School of Physics 'Enrico Fermi': CP Violation: From Quarks to Leptons (2005) pp. 407-438, arXiv:hep-ph/0511213 .

[21] B. R. Safdi, (2022), arXiv:2303.02169 [hep-ph] .

[22] D. J. E. Marsh and A.-R. Pop, Mon. Not. Roy. Astron. Soc. 451, 2479 (2015), arXiv:1502.03456 [astro-ph.CO] .

[23] S. Weinberg, Phys. Rev. Lett. 110, 241301 (2013), arXiv:1305.1971 [astro-ph.CO]

[24] K. Kannike, A. Kubarski, L. Marzola, and A. Racioppi, Phys. Lett. B 792, 74 (2019), arXiv:1810.12689 [hep-ph] .

[25] C. Boehm, M. J. Dolan, and C. McCabe, JCAP 12, 027 (2012), arXiv:1207.0497 [astro-ph.CO] .

[26] A. A. Starobinsky, Phys. Lett. B 91, 99 (1980).

[27] A. H. Guth, Phys. Rev. D 23, 347 (1981).

[28] A. D. Linde, Phys. Lett. B 108, 389 (1982).

[29] A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett. 48, 1220 (1982).

[30] J. Martin, C. Ringeval, and V. Vennin, Phys. Dark Univ. 5-6, 75 (2014), arXiv:1303.3787 [astro-ph.CO] .

[31] P. A. R. Ade et al. (BICEP2, Keck Array), Phys. Rev. Lett. 121, 221301 (2018), arXiv:1810.05216 [astro-ph.CO] .

[32] A. Ghoshal, M. Y. Khlopov, Z. Lalak, and S. Porey, (2023), arXiv:2306.09409 [hep-ph] .

[33] A. Ghoshal, M. Y. Khlopov, Z. Lalak, and S. Porey, (2023), arXiv:2306.08675 [hep-ph] .

[34] D. Clowe, M. Bradac, A. H. Gonzalez, M. Markevitch, S. W. Randall, C. Jones, and D. Zaritsky, Astrophys. J. Lett. 648, L109 (2006), arXiv:astro-ph/0608407 .

[35] Y. B. Zel'dovich and I. D. Novikov, Astronomicheskij Zhurnal 43, 758 (1966).

[36] Y. B. Zel'dovich and I. D. Novikov, Soviet Astron. AJ (Engl. Transl. ), 10, 602 (1967).

[37] S. Hawking, Mon. Not. Roy. Astron. Soc. 152, 75 (1971).

[38] B. J. Carr and S. W. Hawking, Mon. Not. Roy. Astron. Soc. 168, 399 (1974).

[39] J. Garcia-Bellido and E. Ruiz Morales, Phys. Dark Univ. 18, 47 (2017), arXiv:1702.03901 [astro-ph.CO] .

[40] K. Kannike, L. Marzola, M. Raidal, and H. Veermae, JCAP 09, 020 (2017), arXiv:1705.06225 [astro-ph.CO] .

[41] P. Ivanov, P. Naselsky, and I. Novikov, Phys. Rev. D 50, 7173 (1994).

[42] E. Cotner, A. Kusenko, M. Sasaki, and V. Takhistov, JCAP 10, 077 (2019), arXiv:1907.10613 [astro-ph.CO] .

[43] M. Khlopov, B. A. Malomed, and I. B. Zeldovich, Mon. Not. Roy. Astron. Soc. 215, 575 (1985).

[44] S. G. Rubin, M. Y. Khlopov, and A. S. Sakharov, Grav. Cosmol. 6, 51 (2000), arXiv:hep-ph/0005271 .

[45] J. Magana, M. San Martin, J. Sureda, M. Rubio, I. Araya, and N. Padilla, Mon. Not. Roy. Astron. Soc. 520, 4276 (2023), arXiv:2207.13689 [astro-ph.CO] .

[46] B. Carr, M. Raidal, T. Tenkanen, V. Vaskonen, and H. Veermae, Phys. Rev. D 96, 023514 (2017), arXiv:1705.05567 [astro-ph.CO] .

[47] J. C. Niemeyer and K. Jedamzik, Phys. Rev. Lett. 80, 5481 (1998), arXiv:astro-ph/9709072 .

[48] V. De Luca, G. Franciolini, and A. Riotto, Phys. Lett. B 807, 135550 (2020), arXiv:2001.04371 [astro-ph.CO] .

[49] T. Suyama and S. Yokoyama, PTEP 2020, 023E03 (2020), arXiv:1912.04687 [astro-ph.CO] .

[50] A. M. Green and A. R. Liddle, Phys. Rev. D 60, 063509 (1999), arXiv:astro-ph/9901268 .

[51] B. V. Lehmann, S. Profumo, and J. Yant, JCAP 04, 007 (2018), arXiv:1801.00808 [astro-ph.CO] .

[52] G. D. Kribs, A. K. Leibovich, and I. Z. Rothstein, Phys. Rev. D 60, 103510 (1999), arXiv:astro-ph/9904021 .

[53] A. D. Dolgov, M. Kawasaki, and N. Kevlishvili, Nucl. Phys. B 807, 229 (2009), arXiv:0806.2986 [hep-ph] .

[54] S. Bird etal., Phys. DarkUniv. 41, 101231 (2023), arXiv:2203.08967 [hep-ph] .

[55] B. Carr and F. Kuhnel, SciPost Phys. Lect. Notes 48, 1 (2022), arXiv:2110.02821 [astro-ph.CO] .

[56] G. Hutsi, M. Raidal, J. Urrutia, V. Vaskonen, and H. Veermae, Phys. Rev. D 107, 043502(2023), arXiv:2211.02651 [astro-ph.CO] .

[57] M. Sten Delos and J. Silk, Mon. Not. Roy. Astron. Soc. 520, 4370 (2023), arXiv:2210.04904 [astro-ph.CO] .

[58] B. Schwabe, M. Gosenca, C. Behrens, J. C. Niemeyer, and R. Easther, Phys. Rev. D 102, 083518 (2020), arXiv:2007.08256 [astro-ph.CO] .

[59] J. Adamek, C. T. Byrnes, M. Gosenca, and S. Hotchkiss, Phys. Rev. D 100, 023506 (2019), arXiv:1901.08528 [astro-ph.CO] .

[60] M. Y. Khlopov, J. Phys. Conf. Ser. 1690, 012182 (2020), arXiv:2010.14581 [hep-ph] .

[61] X. Chu, Y. Mambrini, J. Quevillon, and B. Zaldivar, JCAP 01, 034 (2014), arXiv:1306.4677 [hep-ph] .

[62] M. Szydagis etal., (2022), arXiv:2211.10726 [hep-ex] .

[63] L. Baudis, J. Hall, K. T. Lesko, and J. L. Orrell, (2022), arXiv:2212.07037 [hep-ex] .

[64] J. Liu (PandaX), in 16th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativis-tic Field Theories (2023).

[65] L. Gu et al. (PandaX), Phys. Rev. Lett. 129, 161803 (2022), arXiv:2205.15771 [hep-ex] .

[66] R. N. Lerner and J. McDonald, Phys. Rev. D 80, 123507 (2009), arXiv:0909.0520 [hep-ph] .

[67] F. Kahlhoefer and J. McDonald, JCAP 11, 015 (2015), arXiv:1507.03600 [astro-ph.CO] .

[68] T. E. Clark, B. Liu, S. T. Love, and T. ter Veldhuis, Phys. Rev. D 80, 075019 (2009), arXiv:0906.5595 [hep-ph] .

[69] V. V. Khoze, JHEP 11, 215 (2013), arXiv:1308.6338 [hep-ph] .

[70] J. P. B. Almeida, N. Bernal, J. Rubio, and T. Tenkanen, JCAP 03, 012 (2019), arXiv:1811.09640 [hep-ph] .

[71] N. Bernal, A. Chatterjee, and A. Paul, JCAP 12, 020 (2018), arXiv:1809.02338 [hep-ph] .

[72] A. Aravind, M. Xiao, and J.-H. Yu, Phys. Rev. D 93, 123513 (2016), [Erratum: Phys.Rev.D 96, 069901 (2017)], arXiv:1512.09126 [hep-ph] .

[73] G. Ballesteros, J. Redondo, A. Ringwald, and C. Tamarit, JCAP 08, 001 (2017), arXiv:1610.01639 [hep-ph] .

[74] D. Borah, P. S. B. Dev, and A. Kumar, Phys. Rev. D 99, 055012 (2019), arXiv:1810.03645 [hep-ph] .

[75] Y. Hamada, H. Kawai, and K.-y. Oda, JHEP 07,026 (2014), arXiv:1404.6141 [hep-ph] .

[76] S. Choubey and A. Kumar, JHEP 11, 080 (2017), arXiv:1707.06587 [hep-ph] .

[77] J. M. Cline, M. Puel, and T. Toma, JHEP 05, 039 (2020), arXiv:2001.11505 [hep-ph] .

[78] T. Tenkanen, JHEP 09, 049 (2016), arXiv:1607.01379 [hep-ph] .

[79] Y. Abe, T. Toma, and K. Yoshioka, JHEP 03, 130 (2021), arXiv:2012.10286 [hep-ph] .

[80] N. Okada, D. Raut, and Q. Shafi, Eur. Phys. J. C 80, 1056 (2020), arXiv:2002.07110 [hep-ph] .

[81] H. Davoudiasl, R. Kitano, T. Li, and H. Murayama, Phys. Lett. B 609, 117 (2005), arXiv:hep-ph/0405097 .

[82] D. Hooper, G. Krnjaic, A. J. Long, and S. D. Mcdermott, Phys. Rev. Lett. 122, 091802 (2019), arXiv:1807.03308 [hep-ph] .

[83] M. Shaposhnikov and I. Tkachev, Phys. Lett. B 639, 414 (2006), arXiv:hep-ph/0604236 .

[84] R. Daido, F. Takahashi, and W. Yin, JCAP 05, 044 (2017), arXiv:1702.03284 [hep-ph] .

[85] Y. Ema, K. Hamaguchi, T. Moroi, and K. Nakayama, JHEP 01, 096 (2017), arXiv:1612.05492 [hep-ph] .

[86] A. Ghoshal, L. Heurtier, and A. Paul, JHEP 12, 105 (2022), arXiv:2208.01670 [hep-ph] .

[87] A. Ghoshal, N. Okada, and A. Paul, Phys. Rev. D 106, 095021 (2022), arXiv:2203.03670 [hep-ph] .

[88] A. Ghoshal, N. Okada, and A. Paul, Phys. Rev. D 106, 055024 (2022), arXiv:2203.00677 [hep-ph] .

[89] G. Ballesteros and C. Tamarit, JHEP 02, 153 (2016), arXiv:1510.05669 [hep-ph] .

[90] V. N. Senoguz and Q. Shafi, Phys. Lett. B 668, 6 (2008), arXiv:0806.2798 [hep-ph]

[91] K. Enqvist and M. Karciauskas, JCAP 02, 034 (2014), arXiv:1312.5944 [astro-ph.CO] .

[92] N. Okada, S. Okada, and D. Raut, Phys. Rev. D 95, 055030 (2017), arXiv:1702.02938 [hep-ph] .

[93] S.-M. Choi and H. M. Lee, Eur. Phys. J. C 76, 303 (2016), arXiv:1601.05979 [hep-ph] .

[94] R. Allahverdi, K. Enqvist, J. Garcia-Bellido, and A. Mazumdar, Phys. Rev. Lett. 97, 191304 (2006), arXiv:hep-ph/0605035 .

[95] J. C. Bueno Sanchez, K. Dimopoulos, and D. H. Lyth, JCAP 01, 015 (2007), arXiv:hep-ph/0608299 .

[96] D. Baumann, A. Dymarsky, I. R. Klebanov, L. McAllister, and P. J. Steinhardt, Phys. Rev. Lett. 99, 141601 (2007), arXiv:0705.3837 [hep-th] .

[97] D. Baumann, A. Dymarsky, I. R. Klebanov, and L. McAllister, JCAP 01, 024 (2008), arXiv:0706.0360 [hep-th] .

[98] M. Badziak and M. Olechowski, JCAP 02, 010 (2009), arXiv:0810.4251 [hep-th] .

[99] K. Enqvist, A. Mazumdar, and P. Stephens, JCAP 06,020 (2010), arXiv:1004.3724 [hep-ph] .

[100] R. Cerezo and J. G. Rosa, JHEP 01, 024 (2013), arXiv:1210.7975 [hep-ph] .

[101] S. Choudhury, A. Mazumdar, and S. Pal, JCAP 07, 041 (2013), arXiv:1305.6398 [hep-ph] .

[102] S. Choudhury and A. Mazumdar, (2014), arXiv:1403.5549 [hep-th] .

[103] N. Okada and D. Raut, Phys. Rev. D 95, 035035 (2017), arXiv:1610.09362 [hep-ph] .

[104] E. D. Stewart, Phys. Lett. B 391, 34 (1997), arXiv:hep-ph/9606241 .

[105] E. D. Stewart, Phys. Rev. D 56, 2019 (1997), arXiv:hep-ph/9703232 .

[106] M. Drees and Y. Xu, JCAP 09, 012 (2021), arXiv:2104.03977 [hep-ph] .

[107] A. Bedroya, R. Brandenberger, M. Loverde, and C. Vafa, Phys. Rev. D101,103502 (2020), arXiv:1909.11106 [hep-th] .

[108] P. Agrawal, G. Obied, P. J. Steinhardt, and C. Vafa, Phys. Lett. B 784, 271 (2018), arXiv:1806.09718 [hep-th] .

[109] J. B. Munoz, E. D. Kovetz, A. Raccanelli, M. Kamionkowski, and J. Silk, JCAP 05, 032 (2017), arXiv:1611.05883 [astro-ph.CO] .

[110] G. D. Coughlan, W. Fischler, E. W. Kolb, S. Raby, and G. G. Ross, Phys. Lett. B 131, 59(1983).

[111] E. Menegoni, M. Archidiacono, E. Calabrese, S. Galli, C. J. A. P. Martins, and A. Melchiorri, Phys. Rev. D 85, 107301 (2012), arXiv:1202.1476 [astro-ph.CO] .

[112] M. Archidiacono, E. Calabrese, and A. Melchiorri, Phys. Rev. D 84, 123008 (2011), arXiv:1109.2767 [astro-ph.CO] .

[113] J. Hasenkamp and J. Kersten, JCAP 08, 024 (2013), arXiv:1212.4160 [hep-ph] .

[114] L. Ackerman, M. R. Buckley, S. M. Carroll, and M. Kamionkowski, Phys. Rev. D 79, 023519 (2009), arXiv:0810.5126 [hep-ph] .

[115] M. Archidiacono, S. Gariazzo, C. Giunti, S. Hannestad, R. Hansen, M. Laveder, and T. Tram, JCAP 08, 067 (2016), arXiv:1606.07673 [astro-ph.CO] .

[116] M. Archidiacono, N. Fornengo, S. Gariazzo, C. Giunti, S. Hannestad, and M. Laveder, JCAP 06, 031 (2014), arXiv:1404.1794 [astro-ph.CO] .

[117] K. J. Bae, H. Baer, and E. J. Chun, JCAP 12, 028 (2013), arXiv:1309.5365 [hep-ph].

[118] E. Di Valentino, A. Melchiorri, and O. Mena, JCAP 11, 018 (2013), arXiv:1304.5981 [astro-ph.CO] .

[119] F. D'Eramo, R. Z. Ferreira, A. Notari, and J. L. Bernal, JCAP 11, 014 (2018), arXiv:1808.07430 [hep-ph] .

[120] E. Calabrese, D. Huterer, E. V. Linder, A. Melchiorri, and L. Pagano, Phys. Rev. D 83, 123504 (2011), arXiv:1103.4132 [astro-ph.CO] .

[121] V. A. Rubakov and D. S. Gorbunov, Introduction to the Theory of the Early Universe: Hot big bang theory (World Scientific, Singapore, 2017).

[122] P. J. E. Peebles, Astrophys. J. Lett. 263, L1 (1982).

[123] L. Perivolaropoulos and F. Skara, New Astron. Rev. 95, 101659 (2022), arXiv:2105.05208 [astro-ph.CO] .

[124] E. W. Kolb, Subnucl. Ser. 45, 337 (2009), arXiv:0709.3102 [astro-ph] .

[125] D. Larson et al., Astrophys. J. Suppl. 192, 16 (2011), arXiv:1001.4635 [astro-ph.CO] .

[126] S. Anselmi, M. F. Carney, J. T. Giblin, S. Kumar, J. B. Mertens, M. O'Dwyer, G. D. Starkman, and C. Tian, JCAP 02, 049 (2023), arXiv:2207.06547 [astro-ph.CO] .

[127] J. J. Bennett, G. Buldgen, M. Drewes, and Y. Y. Y. Wong, JCAP 03, 003 (2020), [Addendum: JCAP 03, A01 (2021)], arXiv:1911.04504 [hep-ph] .

[128] A. Riotto, ICTP Lect. Notes Ser. 14, 317 (2003), arXiv:hep-ph/0210162 .

[129] H. P. Robertson, Astrophys. J. 82, 284 (1935).

[130] H. P. Robertson, Astrophys. J. 83, 187 (1935).

[131] H. P. Robertson, Astrophys. J. 83, 257 (1936).

[132] A. G. Walker, Proceedings of the London Mathematical Society 42, 90 (1937).

[133] D. Baumann, Cosmology (Cambridge University Press, 2022).

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

A. D. Dolgov, Phys. Atom. Nucl. 73, 815 (2010), arXiv:0907.0668 [hep-ph] .

A. D. Dolgov, Phys. Atom. Nucl. 71, 651 (2008), arXiv:hep-ph/0606230 .

A. R. Liddle, in ICTP Summer School in High-Energy Physics and Cosmology (1999) pp. 260-295, arXiv:astro-ph/9901124 .

C. P. Burgess, PoS P 2GC, 008 (2006), arXiv:0708.2865 [hep-th] .

D. Baumann, in Theoretical Advanced Study Institute in Elementary Particle Physics: Physics of the Large and the Small (2011) pp. 523-686, arXiv:0907.5424 [hep-th] .

M. Abramowitz, I. A. Stegun, and R. H. Romer, "Handbook of mathematical functions with formulas, graphs, and mathematical tables," (1988).

V. Mukhanov, Physical Foundations of Cosmology (Cambridge University Press, Oxford, 2005).

L. Husdal, Galaxies 4, 78 (2016), arXiv:1609.04979 [astro-ph.CO] .

A. D. Dolgov, Phys. Rept. 370, 333 (2002), arXiv:hep-ph/0202122 .

C. Bambi and A. D. Dolgov, Introduction to Particle Cosmology, UNITEXT for Physics (Springer, 2015).

A. D. Dolgov and M. Fukugita, JETP Lett. 56, 123 (1992).

A. D. Dolgov and M. Fukugita, Phys. Rev. D 46, 5378 (1992).

C. Bambi, A. D. Dolgov, and K. Freese, JCAP 04, 005 (2007), arXiv:hep-ph/0612018 .

K. A. Olive, in 12th Lake Louise Winter Institute: Particles and the Universe (1997) pp. 60-126, arXiv:astro-ph/9707212 .

C. Pitrou, A. Coc, J.-P. Uzan, and E. Vangioni, Phys. Rept. 754, 1 (2018), arXiv:1801.08023 [astro-ph.CO] .

V. F. Mukhanov, Int. J. Theor. Phys. 43, 669 (2004), arXiv:astro-ph/0303073 .

B. D. Fields and S. Sarkar, (2002).

[151] B. D. Fields, P. Molaro, and S. Sarkar, Chin. Phys. C 38, 339 (2014), arXiv:1412.1408 [astro-ph.CO] .

[152] A. M. Boesgaard and G. Steigman, Ann. Rev. Astron. Astrophys. 23, 319 (1985).

[153] R. V. Wagoner, Astrophys. J. 179, 343 (1973).

[154] M. S. Turner, KICP/UChicago, and T. K. Foundation, (2021), arXiv:2111.14254 [astro-ph.CO] .

[155] A. D. Dolgov, Surveys High Energ. Phys. 17, 91 (2002), arXiv:hep-ph/0208222 .

[156] W. Hu, Annals Phys. 303, 203 (2003), arXiv:astro-ph/0210696 .

[157] G. F. Smoot et al. (COBE), Astrophys. J. Lett. 396, L1 (1992).

[158] C. L. Bennett et al. (WMAP), Astrophys. J. Suppl. 208, 20 (2013), arXiv:1212.5225 [astro-ph.CO] .

[159] A. Paul, Dark matter and neutrinos in cosmology, Ph.D. thesis, Calcutta U. (2022).

[160] A. Mangilli (Planck), IAU Symp. 306, 131 (2014).

[161] Y. Akrami et al. (Planck), Astron. Astrophys. 641, A9 (2020), arXiv:1905.05697 [astro-ph.CO] .

[162] W. Hu and M. J. White, New Astron. 2, 323 (1997), arXiv:astro-ph/9706147 .

[163] D. Baumann et al. (CMBPol Study Team), AIP Conf. Proc. 1141, 10 (2009), arXiv:0811.3919 [astro-ph] .

[164] P. A. Zyla et al. (Particle Data Group), PTEP 2020, 083C01 (2020).

[165] R. L. Workman et al. (Particle Data Group), PTEP 2022, 083C01 (2022).

[166] D. Tong, Cambridge University (2019).

[167] L. Senatore, in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (2017) pp. 447-543, arXiv:1609.00716 [hep-th] .

[168] A. R. Liddle and D. H. Lyth, Cosmological inflation and large scale structure (2000).

[169] D. Baumann, PoS TASI2017, 009 (2018), arXiv:1807.03098 [hep-th] .

[170] W. H. Kinney, (2009), arXiv:0902.1529 [astro-ph.CO] .

[171] S. Tsujikawa, in 2nd Tah Poe School on Cosmology: Modern Cosmology (2003) arXiv:hep-ph/0304257 .

[172] M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018).

[173] V. Demozzi, On inflationary perturbations, Ph.D. thesis, LMU Munich (main) (2011).

[174] S. Hotchkiss, A. Mazumdar, and S. Nadathur, JCAP 02, 008 (2012), arXiv:1110.5389 [astro-ph.CO] .

[175] A. Chatterjee and A. Mazumdar, JCAP 01, 031 (2015), arXiv:1409.4442 [astro-ph.CO] .

[176] A. Chatterjee and A. Mazumdar, Phys. Rev. D 97, 063517 (2018), arXiv:1708.07293 [astro-ph.CO] .

[177] A. D. Linde, Lect. Notes Phys. 738, 1 (2008), arXiv:0705.0164 [hep-th] .

[178] D. J. H. Chung, G. Shiu, and M. Trodden, Phys. Rev. D 68, 063501 (2003), arXiv:astro-ph/0305193 .

[179] D. H. Lyth and A. Riotto, Phys. Rept. 314, 1 (1999), arXiv:hep-ph/9807278 .

[180] Q.-G. Huang, JCAP 11, 004 (2006), arXiv:astro-ph/0610389 .

[181] P. A. R. Ade et al. (BICEP/Keck), in 56th Rencontres de Moriond on Cosmology (2022) arXiv:2203.16556 [astro-ph.CO] .

[182] P. A. R. Ade et al. (BICEP, Keck), Phys. Rev. Lett. 127, 151301 (2021), arXiv:2110.00483 [astro-ph.CO] .

[183] P. Campeti and E. Komatsu, Astrophys. J. 941, 110 (2022), arXiv:2205.05617 [astro-ph.CO] .

[184] A. Arbey and F. Mahmoudi, Prog. Part. Nucl. Phys. 119, 103865 (2021), arXiv:2104.11488 [hep-ph] .

[185] M. Lisanti, in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (2017) pp. 399-446, arXiv:1603.03797 [hep-ph] .

[186] K. A. Olive, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 2002): Particle Physics and Cosmology: The Quest for Physics Beyond the Standard Model(s) (2003) pp. 797-851, arXiv:astro-ph/0301505 .

[187] A. M. Green, SciPostPhys. Lect. Notes 37, 1 (2022), arXiv:2109.05854 [hep-ph] .

[188] R. Massey, T. Kitching, and J. Richard, Rept. Prog. Phys. 73, 086901 (2010), arXiv:1001.1739 [astro-ph.CO] .

[189] A. D. Dolgov, in 6th International Conference on Particle Physics and Astrophysics (2023) arXiv:2301.01365 [astro-ph.CO] .

[190] A. D. Dolgov, J. Phys. Conf. Ser. 1690, 012183 (2020), arXiv:2010.11824 [astro-ph.CO] .

[191] A. D. Dolgov, in 8th International Conference on New Frontiers in Physics (2020) arXiv:2002.10332 [astro-ph.GA] .

[192] A. D. Dolgov, PoS MULTIF2019, 013 (2020), arXiv:1911.02382 [astro-ph.CO] .

[193] A. D. Dolgov, Int. J. Mod. Phys. A 33, 1844029 (2018), arXiv:1808.09909 [astro-ph.CO] .

[194] A. D. Dolgov, in 18th Lomonosov Conference on Elementary Particle Physics (2019) pp. 262-271, arXiv:1712.08789 [astro-ph.CO] .

[195] A. D. Dolgov and S. Porey, Bulg. Astron. J. 34, 2021 (2019), arXiv:1905.10972 [astro-ph.CO] .

[196] V. Kalogera and G. Baym, Astrophys. J. Lett. 470, L61 (1996), arXiv:astro-ph/9608059 .

[197] Q. Ding, Phys. Rev. D 104, 043527 (2021), arXiv:2011.13643 [astro-ph.CO] .

[198] I. Affleck and M. Dine, Nucl. Phys. B 249, 361 (1985).

[199] A. Dolgov and K. Postnov, JCAP 07, 063 (2020), arXiv:2004.11669 [astro-ph.CO]

[200] B. Carr, F. Kuhnel, and M. Sandstad, Phys. Rev. D 94, 083504 (2016), arXiv:1607.06077 [astro-ph.CO] .

[201] A. Chaudhuri and A. Dolgov, J. Exp. Theor. Phys. 133, 552 (2021), arXiv:2001.11219 [astro-ph.CO] .

[202] A. D. Dolgov, A. G. Kuranov, N. A. Mitichkin, S. Porey, K. A. Postnov, O. S. Sazhina, and I. V. Simkin, JCAP 12, 017 (2020), arXiv:2005.00892 [astro-ph.CO]

[203] S. Blinnikov, A. Dolgov, N. K. Porayko, and K. Postnov, JCAP 11, 036 (2016), arXiv:1611.00541 [astro-ph.HE] .

[204] F. Ozel, D. Psaltis, R. Narayan, and J. E. McClintock, Astrophys. J. 725, 1918 (2010), arXiv:1006.2834 [astro-ph.GA] .

[205] L. Kreidberg, C. D. Bailyn, W. M. Farr, and V. Kalogera, Astrophys. J. 757, 36 (2012), arXiv:1205.1805 [astro-ph.HE] .

[206] W. M. Farr, N. Sravan, A. Cantrell, L. Kreidberg, C. D. Bailyn, I. Mandel, and V. Kalogera, Astrophys. J. 741, 103 (2011), arXiv:1011.1459 [astro-ph.GA] .

[207] N. Aghanim et al. (Planck), Astron. Astrophys. 641, A6 (2020), [Erratum: As-tron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO] .

[208] B. T. Dullo, A. W. Graham, and J. H. Knapen, Mon. Not. Roy. Astron. Soc. 471, 2321 (2017), arXiv:1707.02277 [astro-ph.GA] .

[209] J. E. Greene, Nature Commun. 3, 1304 (2012), arXiv:1211.7082 [astro-ph.CO] .

[210] L. Ferrarese and D. Merritt, Astrophys. J. Lett. 539, L9 (2000), arXiv:astro-ph/0006053 .

[211] K. Gebhardt et al., Astrophys. J. Lett. 539, L13 (2000), arXiv:astro-ph/0006289 .

[212] A. W. Graham, P. Erwin, N. Caon, and I. Trujillo, Astrophys. J. Lett. 563, L11 (2001), arXiv:astro-ph/0111152.

[213] M. Volonteri, F. Haardt, and P. Madau, Astrophys. J. 582, 559 (2003), arXiv:astro-ph/0207276 .

[214] E. Banados etal., Nature 553, 473 (2018), arXiv:1712.01860 [astro-ph.GA] .

[215] C. J. Conselice, A. Wilkinson, K. Duncan, and A. Mortlock, Astrophys. J. 830, 83 (2016).

[216] H.-A. Shinkai, N. Kanda, and T. Ebisuzaki, Astrophys. J. 835, 276 (2017), arXiv:1610.09505 [astro-ph.GA] .

[217] M. Mezcua, F. Civano, S. Marchesi, H. Suh, G. Fabbiano, and M. Volonteri, Mon. Not. Roy. Astron. Soc. 478, 2576 (2018).

[218] H.-Y. Liu, W. Yuan, X.-B. Dong, H. Zhou, and W.-J. Liu, Astrophys. J. Suppl. 235, 40 (2018), arXiv:1803.04330 [astro-ph.GA] .

[219] B. P. Abbott etal. (LIGO Scientific, Virgo), Phys. Rev. Lett. 116, 241102 (2016), arXiv:1602.03840 [gr-qc] .

[220] T. D. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. X 6, 041014 (2016), arXiv:1606.01210 [gr-qc] .

[221] S. Bird, I. Cholis, J. B. Munoz, Y. Ali-Haimoud, M. Kamionkowski, E. D. Kovetz, A. Raccanelli, and A. G. Riess, Phys. Rev. Lett. 116, 201301 (2016), arXiv:1603.00464 [astro-ph.CO] .

[222] B. P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. X 9, 031040 (2019), arXiv:1811.12907 [astro-ph.HE] .

[223] A. H. Nitz, T. Dent, G. S. Davies, S. Kumar, C. D. Capano, I. Harry, S. Moz-zon, L. Nuttall, A. Lundgren, and M. Tapai, Astrophys. J. 891, 123 (2020), arXiv:1910.05331 [astro-ph.HE] .

[224] R. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. D 102, 043015 (2020), arXiv:2004.08342 [astro-ph.HE] .

[225] Y. Ali-Haimoud, E. D. Kovetz, and M. Kamionkowski, Phys. Rev. D 96, 123523 (2017), arXiv:1709.06576 [astro-ph.CO] .

[226] M. Mirbabayi, A. Gruzinov, and J. Norena, JCAP 03, 017 (2020), arXiv:1901.05963 [astro-ph.CO] .

[227] K. Postnov and N. Mitichkin, JCAP 06, 044 (2019), arXiv:1904.00570 [astro-ph.HE] .

[228] P. Davis, U. Kolb, and C. Knigge, Monthly Notices of the Royal Astronomical Society 419, 287 (2012).

[229] R. F. Webbink, (2007), 10.1007/978-1-4020-6544-6_13, arXiv:0704.0280 [astro-ph] .

[230] C. Alcock et al. (Supernova Cosmology Project), Nature 365, 621 (1993), arXiv:astro-ph/9309052.

[231] B. Paczynski, Astrophys. J. 304, 1 (1986).

[232] M. R. Pratt et al., Nucl. Phys. B Proc. Suppl. 51, 131 (1996), arXiv:astro-ph/9606134 .

[233] G. Chabrier, L. Segretain, and D. Mera, Astrophys. J. Lett. 468, L21 (1996), arXiv:astro-ph/9606083 .

[234] B. D. Fields, K. Freese, and D. S. Graff, Astrophys. J. 534, 265 (2000), arXiv:astro-ph/9904291 .

[235] M. R. Pratt et al., AIP Conf. Proc. 342, 106 (1995).

[236] P. Tisserand et al. (EROS-2), Astron. Astrophys. 469, 387 (2007), arXiv:astro-ph/0607207 .

[237] S. Calchi Novati, S. Mirzoyan, P. Jetzer, and G. Scarpetta, Mon. Not. Roy. Astron. Soc. 435, 1582 (2013), arXiv:1308.4281 [astro-ph.GA] .

[238] G. Ingrosso, S. Calchi Novati, F. De Paolis, P. Jetzer, A. A. Nucita, G. Scarpetta, and F. Strafella, Astron. Astrophys. 462, 895 (2007), arXiv:astro-ph/0610239 .

[239] A. Riffeser, S. Seitz, and R. Bender, Astrophys. J. 684, 1093 (2008), arXiv:0805.0137 [astro-ph] .

[240] C. H. Lee, A. Riffeser, S. Seitz, R. Bender, and J. Koppenhoefer, Astrophys. J. 806, 161 (2015), arXiv:1504.07246 [astro-ph.GA] .

[241] H. Niikura etal., Nature Astron. 3, 524 (2019), arXiv:1701.02151 [astro-ph.CO] .

[242] H. Niikura, M. Takada, S. Yokoyama, T. Sumi, and S. Masaki, Phys. Rev. D 99, 083503 (2019), arXiv:1901.07120 [astro-ph.CO] .

[243] M. R. S. Hawkins, Nature 366, 242 (1993).

[244] J. Calcino, J. Garcia-Bellido, and T. M. Davis, Mon. Not. Roy. Astron. Soc. 479, 2889 (2018), arXiv:1803.09205 [astro-ph.CO] .

[245] L. Wyrzykowski and I. Mandel, Astron. Astrophys. 636, A20 (2020), arXiv:1904.07789 [astro-ph.SR] .

[246] K. Griest, A. M. Cieplak, and M. J. Lehner, Phys. Rev. Lett. 111, 181302 (2013).

[247] K. Griest, A. M. Cieplak, and M. J. Lehner, Astrophys. J. 786, 158 (2014), arXiv:1307.5798 [astro-ph.CO] .

[248] M. Oguri, J. M. Diego, N. Kaiser, P. L. Kelly, and T. Broadhurst, Phys. Rev. D 97, 023518 (2018), arXiv:1710.00148 [astro-ph.CO] .

[249] A. Katz, J. Kopp, S. Sibiryakov, and W. Xue, JCAP 12, 005 (2018), arXiv:1807.11495 [astro-ph.CO] .

[250] M. Zumalacarregui and U. Seljak, Phys. Rev. Lett. 121, 141101 (2018), arXiv:1712.02240 [astro-ph.CO] .

[251] V. S. Berezinsky, V. I. Dokuchaev, and Y. N. Eroshenko, Phys. Usp. 57, 1 (2014), arXiv:1405.2204 [astro-ph.HE] .

[252] K. M. Belotsky, V. I. Dokuchaev, Y. N. Eroshenko, E. A. Esipova, M. Y. Khlopov, L. A. Khromykh, A. A. Kirillov, V. V. Nikulin, S. G. Rubin, and I. V. Svadkovsky, Eur. Phys. J. C 79, 246 (2019), arXiv:1807.06590 [astro-ph.CO] .

[253] V. Desjacques and A. Riotto, Phys. Rev. D 98, 123533 (2018), arXiv:1806.10414 [astro-ph.CO] .

[254] J. R. Chisholm, Phys. Rev. D 73, 083504 (2006), arXiv:astro-ph/0509141 .

[255] T. Matsubara, T. Terada, K. Kohri, and S. Yokoyama, Phys. Rev. D 100, 123544 (2019), arXiv:1909.04053 [astro-ph.CO] .

[256] M. Celoria, R. Oliveri, A. Sesana, and M. Mapelli (2018) arXiv:1807.11489 [astro-ph.GA] .

[257] K. J. Bae, M. Park, and M. Zhang, Phys. Rev. D 101, 115036 (2020), arXiv:2001.02142 [hep-ph] .

[258] N. Bhaumik and R. K. Jain, JCAP 01, 037 (2020), arXiv:1907.04125 [astro-ph.CO] .

[259] N. Bernal and Y. Xu, Eur. Phys. J. C 81, 877 (2021), arXiv:2106.03950 [hep-ph] .

[260] A. Ghoshal, G. Lambiase, S. Pal, A. Paul, and S. Porey, JHEP 09, 231 (2022), arXiv:2206.10648 [hep-ph] .

[261] A. Ghoshal, G. Lambiase, S. Pal, A. Paul, and S. Porey, in 25th Workshop on What Comes Beyond the Standard Models? (2022) arXiv:2211.15061 [astro-ph.CO] .

[262] A. Ghoshal, G. Lambiase, S. Pal, A. Paul, and S. Porey, Symmetry 15, 543 (2023).

[263] G. Barenboim, JHEP 03, 102 (2009), arXiv:0811.2998 [hep-ph] .

[264] W. A. Bardeen, C. T. Hill, and M. Lindner, Phys. Rev. D 41, 1647 (1990).

[265] J. R. Bhatt and U. Sarkar, Phys. Rev. D 80, 045016 (2009), arXiv:0805.2482 [hep-ph] .

[266] J. R. Bhatt, B. R. Desai, E. Ma, G. Rajasekaran, and U. Sarkar, Phys. Lett. B 687, 75 (2010), arXiv:0911.5012 [hep-ph] .

[267] G. Barenboim and J. Rasero, JHEP 03, 097 (2011), arXiv:1009.3024 [hep-ph] .

[268] G. Barenboim, Phys. Rev. D 82, 093014 (2010), arXiv:1009.2504 [hep-ph] .

[269] G. Dvali and L. Funcke, Phys. Rev. D 93, 113002 (2016), arXiv:1602.03191 [hep-ph] .

[270] M. U. Rehman, Q. Shafi, and J. R. Wickman, Phys. Lett. B 683, 191 (2010), arXiv:0908.3896 [hep-ph] .

[271] G. R. Dvali, Q. Shafi, and R. K. Schaefer, Phys. Rev. Lett. 73, 1886 (1994), arXiv:hep-ph/9406319 .

[272] E. J. Copeland, A. R. Liddle, D. H. Lyth, E. D. Stewart, and D. Wands, Phys. Rev. D 49, 6410 (1994), arXiv:astro-ph/9401011 .

[273] G. Lazarides, Lect. Notes Phys. 592, 351 (2002), arXiv:hep-ph/0111328 .

[274] F. Takahashi, Phys. Lett. B 693, 140 (2010), arXiv:1006.2801 [hep-ph] .

[275] H. Davoudiasl, Phys. Rev. D 101, 115024 (2020), arXiv:2003.04908 [hep-ph] .

[276] S. Iso, K. Kohri, and K. Shimada, Phys. Rev. D 91, 044006 (2015), arXiv:1408.2339 [hep-ph] .

[277] K. Kaneta, O. Seto, and R. Takahashi, Phys. Rev. D 97, 063004 (2018), arXiv:1708.06455 [hep-ph] .

[278] D. H. Lyth and A. R. Liddle, The primordial density perturbation: Cosmology, inflation and the origin of structure (2009).

[279] C. Germani and T. Prokopec, Phys. Dark Univ. 18, 6 (2017), arXiv:1706.04226 [astro-ph.CO] .

[280] K. Dimopoulos, Phys. Lett. B 775, 262 (2017), arXiv:1707.05644 [hep-ph] .

[281] C. Pattison, V. Vennin, H. Assadullahi, and D. Wands, JCAP 08, 048 (2018), arXiv:1806.09553 [astro-ph.CO] .

[282] R. Penco, (2020), arXiv:2006.16285 [hep-th] .

[283] D. H. Lyth and E. D. Stewart, Phys. Rev. D 53,1784 (1996), arXiv:hep-ph/9510204

[284] M. Kawasaki, T. Takahashi, and S. Yokoyama, JCAP 12, 012 (2009), arXiv:0910.3053 [hep-th] .

[285] P. Binetruy and M. K. Gaillard, Phys. Rev. D 34, 3069 (1986).

[286] G. Lazarides, C. Panagiotakopoulos, and Q. Shafi, Phys. Rev. Lett. 56, 557 (1986).

[287] G. Lazarides, C. Panagiotakopoulos, and Q. Shafi, Phys. Rev. Lett. 58, 1707 (1987).

[288] G. Lazarides and Q. Shafi, Nucl. Phys. B 392, 61 (1993).

[289] A. Jokinen and A. Mazumdar, Phys. Lett. B 597, 222 (2004), arXiv:hep-th/0406074 .

[290] B. A. Bassett, S. Tsujikawa, and D. Wands, Rev. Mod. Phys. 78, 537 (2006), arXiv:astro-ph/0507632.

[291] M. A. G. Garcia, Y. Mambrini, K. A. Olive, and M. Peloso, Phys. Rev. D 96, 103510 (2017), arXiv:1709.01549 [hep-ph] .

[292] S. Davidson and S. Sarkar, JHEP 11, 012 (2000), arXiv:hep-ph/0009078 .

[293] K. Harigaya and K. Mukaida, JHEP 05, 006 (2014), arXiv:1312.3097 [hep-ph] .

[294] K. Mukaida and M. Yamada, JCAP 02, 003 (2016), arXiv:1506.07661 [hep-ph] .

[295] J. Ellis, M. A. G. Garcia, D. V. Nanopoulos, K. A. Olive, and M. Peloso, JCAP 03, 008 (2016), arXiv:1512.05701 [astro-ph.CO] .

[296] E. W. Kolb, A. Notari, and A. Riotto, Phys. Rev. D 68, 123505 (2003), arXiv:hep-ph/0307241 .

[297] K. Enqvist, in 2010 European School of High Energy Physics (2012) arXiv:1201.6164 [gr-qc] .

[298] M. A. G. Garcia, K. Kaneta, Y. Mambrini, and K. A. Olive, Phys. Rev. D 101, 123507 (2020), arXiv:2004.08404 [hep-ph] .

[299] M. A. G. Garcia, K. Kaneta, Y. Mambrini, and K. A. Olive, JCAP 04, 012 (2021), arXiv:2012.10756 [hep-ph] .

[300] N. Bernal, F. Elahi, C. Maldonado, and J. Unwin, JCAP 11, 026 (2019), arXiv:1909.07992 [hep-ph] .

[301] K. D. Lozanov, (2019), arXiv:1907.04402 [astro-ph.CO] .

[302] Y. Mambrini and K. A. Olive, Phys. Rev. D 103, 115009 (2021), arXiv:2102.06214 [hep-ph] .

[303] G. F. Giudice, E. W. Kolb, and A. Riotto, Phys. Rev. D 64, 023508 (2001), arXiv:hep-ph/0005123 .

[304] M. Dijkstra, (2017), arXiv:1704.03416 [astro-ph.GA] .

[305] P. Murdin, Encyclopedia of Astronomy & Astrophysics (CRC Press, 2001).

[306] M. Viel, G. D. Becker, J. S. Bolton, and M. G. Haehnelt, Phys. Rev. D 88, 043502 (2013), arXiv:1306.2314 [astro-ph.CO] .

[307] N. Palanque-Delabrouille, C. Yeche, N. Schöneberg, J. Lesgourgues, M. Walther, S. Chabanier, and E. Armengaud, JCAP 04, 038 (2020), arXiv:1911.09073 [astro-ph.CO] .

[308] A. Garzilli, A. Magalich, O. Ruchayskiy, and A. Boyarsky, Mon. Not. Roy. Astron. Soc. 502, 2356 (2021), arXiv:1912.09397 [astro-ph.CO] .

[309] K. J. Bae, A. Kamada, S. P. Liew, and K. Yanagi, JCAP 01, 054 (2018), arXiv:1707.06418 [hep-ph] .

[310] R. Murgia, A. Merle, M. Viel, M. Totzauer, and A. Schneider, JCAP 11, 046 (2017), arXiv:1704.07838 [astro-ph.CO] .

[311] J. Heeck and D. Teresi, Phys. Rev. D 96, 035018 (2017), arXiv:1706.09909 [hep-ph] .

[312] S. Boulebnane, J. Heeck, A. Nguyen, and D. Teresi, JCAP 04, 006 (2018), arXiv:1709.07283 [hep-ph] .

[313] I. Baldes, Q. Decant, D. C. Hooper, and L. Lopez-Honorez, JCAP 08, 045 (2020), arXiv:2004.14773 [astro-ph.CO] .

[314] G. Ballesteros, M. A. G. Garcia, and M. Pierre, JCAP 03, 101 (2021), arXiv:2011.13458 [hep-ph] .

[315] F. D'Eramo and A. Lenoci, JCAP 10, 045 (2021), arXiv:2012.01446 [hep-ph] .

[316] Q. Decant, J. Heisig, D. C. Hooper, and L. Lopez-Honorez, JCAP 03, 041 (2022), arXiv:2111.09321 [astro-ph.CO] .

[317] L. Caloni, M. Gerbino, M. Lattanzi, and L. Visinelli, JCAP 09, 021 (2022), arXiv:2205.01637 [astro-ph.CO] .

[318] G. Steigman, Phys. Rev. D 87, 103517 (2013), arXiv:1303.0049 [astro-ph.CO] .

[319] X. Luo, W. Rodejohann, and X.-J. Xu, JCAP 06, 058 (2020), arXiv:2005.01629 [hep-ph] .

[320] X. Luo, W. Rodejohann, and X.-J. Xu, JCAP 03, 082 (2021), arXiv:2011.13059 [hep-ph] .

[321] G. Mangano, G. Miele, S. Pastor, and M. Peloso, Phys. Lett. B 534, 8 (2002), arXiv:astro-ph/0111408 .

[322] A. Paul, A. Ghoshal, A. Chatterjee, and S. Pal, Eur. Phys. J. C 79, 818 (2019), arXiv:1808.09706 [astro-ph.CO] .

[323] T. Tram, R. Vallance, and V. Vennin, JCAP 01, 046 (2017), arXiv:1606.09199 [astro-ph.CO] .

[324] G. Mangano, G. Miele, S. Pastor, T. Pinto, O. Pisanti, and P. D. Serpico, Nucl. Phys. B 729, 221 (2005), arXiv:hep-ph/0506164 .

[325] M. Escudero Abenza, JCAP 05, 048 (2020), arXiv:2001.04466 [hep-ph] .

[326] P. F. de Salas and S. Pastor, JCAP 07, 051 (2016), arXiv:1606.06986 [hep-ph] .

[327] K. Abazajian etal., (2019), arXiv:1907.04473 [astro-ph.IM] .

[328] K. N. Abazajian and J. Heeck, Phys. Rev. D 100, 075027 (2019), arXiv:1908.03286 [hep-ph] .

[329] C. M. Ho and R. J. Scherrer, Phys. Rev. D 87, 023505 (2013), arXiv:1208.4347 [astro-ph.CO] .

[330] S. Roy Choudhury, S. Hannestad, and T. Tram, JCAP 10, 018 (2022), arXiv:2207.07142 [astro-ph.CO] .

[331] D. Cadamuro and J. Redondo, J. Phys. Conf. Ser. 375, 022002 (2012).

[332] M. Berbig and A. Ghoshal, JHEP 05, 172 (2023), arXiv:2301.05672 [hep-ph] .

[333] M. Gerbino etal., (2022), arXiv:2203.07377 [hep-ph] .

[334] L. Balkenhol etal. (SPT-3G), Phys. Rev. D 104, 083509 (2021), arXiv:2103.13618 [astro-ph.CO] .

[335] J. Delabrouille et al. (CORE), JCAP 04, 014 (2018), arXiv:1706.04516 [astro-ph.IM] .

[336] "CMB-Bharat collaboration," http://cmb-bharat.in/.

[337] S. Hanany etal. (NASA PICO), (2019), arXiv:1902.10541 [astro-ph.IM] .

[338] K. Abazajian etal. (CMB-S4), (2022), arXiv:2203.08024 [astro-ph.CO] .

[339] N. Sehgal etal., (2019), arXiv:1906.10134 [astro-ph.CO] .

[340] S. Aiolaetal. (CMB-HD), (2022), arXiv:2203.05728 [astro-ph.CO] .

[341] A. Cheek, L. Heurtier, Y. F. Perez-Gonzalez, and J. Turner, Phys. Rev. D 106, 103012 (2022), arXiv:2207.09462 [astro-ph.CO] .

[342] S. Bashinsky and U. Seljak, Phys. Rev. D 69, 083002 (2004), arXiv:astro-ph/0310198 .

[343] C. Patrignani et al. (Particle Data Group), Chin. Phys. C 40, 100001 (2016).

[344] J. Lesgourgues, G. Mangano, G. Miele, and S. Pastor, Neutrino Cosmology (Cambridge University Press, 2013).

[345] Z. Hou, R. Keisler, L. Knox, M. Millea, and C. Reichardt, Phys. Rev. D 87, 083008 (2013), arXiv:1104.2333 [astro-ph.CO] .

[346] B. Follin, L. Knox, M. Millea, and Z. Pan, Phys. Rev. Lett. 115, 091301 (2015), arXiv:1503.07863 [astro-ph.CO] .

[347] P. A. R. Ade et al. (Planck), Astron. Astrophys. 594, A13 (2016), arXiv:1502.01589 [astro-ph.CO] .

[348] R.-Y. Guo and X. Zhang, Eur. Phys. J. C 77, 882 (2017), arXiv:1704.04784 [astro-ph.CO] .

[349] D. J. E. Marsh, Phys. Rept. 643, 1 (2016), arXiv:1510.07633 [astro-ph.CO] .

[350] K. Kohri, C.-M. Lin, and D. H. Lyth, JCAP 12, 004 (2007), arXiv:0707.3826 [hep-ph] .

[351] L. Boubekeur and D. H. Lyth, JCAP 07, 010 (2005), arXiv:hep-ph/0502047 .

[352] D. J. E. Marsh, in 13th Patras Workshop onAxions, WIMPs and WISPs (2018) pp. 59-74, arXiv:1712.03018 [hep-ph] .

[353] K. Freese, J. A. Frieman, and A. V. Olinto, Phys. Rev. Lett. 65, 3233 (1990).

[354] J. E. Kim, H. P. Nilles, and M. Peloso, JCAP 01, 005 (2005), arXiv:hep-ph/0409138 .

[355] G. Barenboim, E. J. Chun, and H. M. Lee, Phys. Lett. B 730, 81 (2014), arXiv:1309.1695 [hep-ph] .

[356] N. Okada, V. N. Senoguz, and Q. Shafi, Turk. J. Phys. 40, 150 (2016), arXiv:1403.6403 [hep-ph] .

[357] R. Kallosh and A. Linde, JCAP 09, 030 (2019), arXiv:1906.02156 [hep-th] .

[358] A. Mazumdar, S. Mohanty, and P. Parashari, Phys. Rev. D 101, 083521 (2020), arXiv:1911.08512 [astro-ph.CO] .

[359] K. S. Stelle, Phys. Rev. D 16, 953 (1977).

[360] K. S. Stelle, Gen. Rel. Grav. 9, 353 (1978).

[361] M. Brinkmann, M. Cicoli, and P. Zito, JHEP 09, 038 (2023), arXiv:2305.05703 [hep-th] .

[362] Y. Aldabergenov, R. Ishikawa, S. V. Ketov, and S. I. Kruglov, Phys. Rev. D 98, 083511 (2018), arXiv:1807.08394 [hep-th] .

[363] C. Pallis and N. Toumbas, Adv. High Energy Phys. 2017, 6759267 (2017), arXiv:1612.09202 [hep-ph] .

[364] K. Freese, in 37th Yamada Conference: Evolution of the Universe and its Observational Quest (1993) pp. 49-58, arXiv:astro-ph/9310012 .

[365] N. K. Stein and W. H. Kinney, JCAP 01, 022 (2022), arXiv:2106.02089 [astro-ph.CO] .

[366] M. Drewes, J. U. Kang, and U. R. Mun, JHEP 11, 072 (2017), arXiv:1708.01197 [astro-ph.CO] .

[367] R. Jinno, T. Moroi, and K. Nakayama, Phys. Rev. D 86, 123502 (2012), arXiv:1208.0184 [astro-ph.CO] .

[368] B. Barman, N. Bernal, Y. Xu, and O. Zapata, JCAP 07, 019 (2022), arXiv:2202.12906 [hep-ph] .

[369] E. Di Valentino and F. R. Bouchet, JCAP 10, 011 (2016), arXiv:1609.00328 [astro-ph.CO] .

[370] N. Aghanim et al. (Planck), Astron. Astrophys. 594, A11 (2016), arXiv:1507.02704 [astro-ph.CO] .

[371] N. Aghanim et al. (Planck), Astron. Astrophys. 596, A107 (2016), arXiv:1605.02985 [astro-ph.CO] .

[372] P. A. R. Ade et al. (BICEP2, Planck), Phys. Rev. Lett. 114, 101301 (2015), arXiv:1502.00612 [astro-ph.CO] .

[373] M. Drewes, JCAP 09, 069 (2022), arXiv:1903.09599 [astro-ph.CO] .

[374] R. Allahverdi, R. Brandenberger, F.-Y. Cyr-Racine, and A. Mazumdar, Ann. Rev. Nucl. Part. Sci. 60, 27 (2010), arXiv:1001.2600 [hep-th] .

[375] A. Ghoshal, Z. Lalak, and S. Porey, Phys. Rev. D 108, 063030 (2023), arXiv:2302.03268 [hep-ph] .

[376] E. Di Valentino and L. Mersini-Houghton, JCAP 03, 002 (2017), arXiv:1612.09588 [astro-ph.CO] .

[377] K. Freese and W. H. Kinney, JCAP 03,044 (2015), arXiv:1403.5277 [astro-ph.CO]

[378] G. Panotopoulos, Astropart. Phys. 128, 102559 (2021).

[379] K. Dimopoulos, C. Owen, and A. Racioppi, Astropart. Phys. 103, 16 (2018), arXiv:1706.09735 [hep-ph] .

[380] A. Ghoshal, D. Nanda, and A. K. Saha, (2022), arXiv:2210.14176 [hep-ph] .

[381] A. Dolgov and K. Postnov, JCAP 04, 036 (2017), arXiv:1702.07621 [astro-ph.CO]

[382] T. D. Brandt, Astrophys. J. Lett. 824, L31 (2016), arXiv:1605.03665 [astro-ph.GA]

[383] M. Raidal, C. Spethmann, V. Vaskonen, and H. Veermae, JCAP 02, 018 (2019), arXiv:1812.01930 [astro-ph.CO] .

[384] J. Manshanden, D. Gaggero, G. Bertone, R. M. T. Connors, and M. Ricotti, JCAP 06, 026 (2019), arXiv:1812.07967 [astro-ph.HE] .

[385] L. Wyrzykowski et al., Mon. Not. Roy. Astron. Soc. 416, 2949 (2011), arXiv:1106.2925 [astro-ph.GA] .

[386] B. P. Abbott etal. (LIGO Scientific, Virgo), Phys. Rev. Lett. 121, 231103 (2018), arXiv:1808.04771 [astro-ph.CO] .

[387] S. Calchi Novati and L. Mancini, Mon. Not. Roy. Astron. Soc. 416, 1292 (2011), arXiv:1105.4615 [astro-ph.GA] .

[388] L. Chen, Q.-G. Huang, and K. Wang, JCAP 12, 044 (2016), arXiv:1608.02174 [astro-ph.CO] .

[389] M. Sasaki, T. Suyama, T. Tanaka, and S. Yokoyama, Class. Quant. Grav. 35, 063001 (2018), arXiv:1801.05235 [astro-ph.CO] .

[390] D. P. Quinn, M. I. Wilkinson, M. J. Irwin, J. Marshall, A. Koch, and V. Belokurov, Mon. Not. Roy. Astron. Soc. 396, 11 (2009), arXiv:0903.1644 [astro-ph.GA] .

[391] Y. Ali-Haimoud and M. Kamionkowski, Phys. Rev. D 95, 043534 (2017), arXiv:1612.05644 [astro-ph.CO] .

[392] V. Poulin, P. D. Serpico, F. Calore, S. Clesse, and K. Kohri, Phys. Rev. D 96, 083524 (2017), arXiv:1707.04206 [astro-ph.CO] .

[393] D. Gaggero, G. Bertone, F. Calore, R. M. T. Connors, M. Lovell, S. Markoff, and E. Storm, Phys. Rev. Lett. 118, 241101 (2017), arXiv:1612.00457 [astro-ph.HE] .

[394] Y. Inoue and A. Kusenko, JCAP 10, 034 (2017), arXiv:1705.00791 [astro-ph.CO]

[395] M. Ricotti, J. P. Ostriker, and K. J. Mack, Astrophys. J. 680, 829 (2008), arXiv:0709.0524 [astro-ph] .

[396] R. Kallosh and A. Linde, Phys. Rev. D 100, 123523 (2019), arXiv:1909.04687 [hep-th] .

[397] R. Kallosh and A. Linde, JCAP 12, 008 (2021), arXiv:2110.10902 [astro-ph.CO] .

[398] D. Griffiths, Introduction to elementary particles (2008).

[399] J. Ellis, M. A. G. Garcia, D. V. Nanopoulos, K. A. Olive, and S. Verner, Phys. Rev. D 105, 043504 (2022), arXiv:2112.04466 [hep-ph] .

[400] S. Hannestad, Phys. Rev. D 70, 043506 (2004), arXiv:astro-ph/0403291 .