Search

The curvature perturbation in a model of constant-roll (CR) inflation is interpreted in view of the logarithmic duality discovered in Ref. [1] according to the $\delta N$ formalism. We confirm that the critical value $\beta:=\ddot{\varphi}/(H\dot{\varphi})=-3/2$ determining whether the CR condition is stable or not is understood as the point at which the dual solutions, i.e., the attractor and non-attractor solutions of the field equation, are interchanged. For the attractor-solution domination, the curvature perturbation in the CR model is given by a simple logarithmic mapping of a Gaussian random field, which can realise both the exponential tail (i.e., the single exponential decay) and the Gumbel-distribution-like tail (i.e., the double exponential decay) of the probability density function, depending on the value of $\beta$. Such a tail behaviour is important for, e.g., the estimation of the primordial black hole abundance., Comment: 14 pages, 4 figures

We investigate the null test of cosmic accelerated expansion by using the Baryon Acoustic Oscillation (BAO) measurements released by the Dark Energy Spectroscopic Instrument, and we find that the latest BAO data alone can provide strong model-independent evidence for the existence of accelerated expansion in the Universe. Using Gaussian Process reconstruction, we derive the deceleration parameter $q(z)$ from the BAO data, revealing that accelerated expansion persisted until $z \lesssim 0.833$. By further incorporating data from Cosmic Chronometers and 6 expansion rate measured by type Ia supernovae, we find that accelerated expansion continued until $z \lesssim 0.417$., Comment: 15 pages, 6 figures

We discuss a mechanism of primordial black hole (PBH) formation that does not require specific features in the inflationary potential, revisiting previous literature. In this mechanism, a light spectator field evolves stochastically during inflation and remains subdominant during the post-inflationary era. Even though the curvature power spectrum stays small at all scales, rare perturbations of the field probe a local maximum in its potential, leading to non-Gaussian tails in the distribution of curvature fluctuations, and to copious PBH production. For a concrete axion-like particle (ALP) scenario we analytically determine the distribution of the compaction function for perturbations, showing that it is characterized by a heavy tail, which produces an extended PBH mass distribution. We find the ALP mass and decay constant to be correlated with the PBH mass, for instance, an ALP with a mass $m_a = 5.4 \times 10^{14}$ eV and a decay constant $f_a = 4.6 \times 10^{-5} Mpl$ can lead to PBHs of mass $M_{\rm PBH} = 10^{21}$ g as the entire dark matter (DM) of the universe, and is testable in future PBH observations via lensing in the NGRST and mergers detectable in the LISA and ET Gravitational Waves (GW) detectors. We then extend our analysis to mixed ALP and PBH dark matter and Higgs-like spectator fields. We find that PBHs cluster strongly over all cosmological scales, clashing with CMB isocurvature bounds. We argue that this problem is shared by all PBH production from inflationary models that depend solely on large non-Gaussianity without a peak in the curvature power spectrum and discuss possible remedies., Comment: 30 pages + Appendices, 7 figures; comments are welcome !

We study the Primordial Black Hole (PBH) reheating scenario, where PBHs originate in a general cosmological background. In this scenario, ultralight PBHs with masses $M\lesssim 10^8$g temporarily dominate the Universe and reheat it via Hawking radiation before Big Bang Nucleosynthesis (BBN). We investigate whether the induced Gravitational Wave (GW) spectrum associated with PBH reheating contains information about the pre-PBH-dominated stage, namely the initial equation of state $w$ (after inflation). We first derive the transfer functions of curvature fluctuations for general $w$ with adiabatic and isocurvature initial conditions. We find that, in general, a stiffer equation of state enhances the induced GW amplitude as it allows for a longer PBH dominated phase compared to the radiation dominated case. We also find that the spectral slope of GWs induced by primordial curvature fluctuations is sensitive to $w$, while the spectral slope of GWs induced by PBH number density fluctuations is not. Lastly, we derive constraints of the initial PBH abundance as a function of $w$, using BBN and Cosmic Microwave Background (CMB) observations. A stiffer equation of state leads to stricter constraints on the initial energy density fraction, as induced GWs are enhanced. Interestingly, we find that such induced GW signals may enter the observational window of several future GW detectors, such as LISA and the Einstein Telescope. Our formulas, especially the curvature fluctuation transfer functions, are applicable to any early matter-dominated universe scenario., Comment: 32 pages + appendices, 9 figures

Spectral distortions of the cosmic microwave background (CMB) provide stringent constraints on energy and entropy production in the post-BBN (Big Bang Nucleosynthesis) era. This has been used to constrain dark photon models with COBE/FIRAS and forecast the potential gains with future CMB spectrometers. Here, we revisit these constraints by carefully considering the photon to dark photon conversion process and evolution of the distortion signal. Previous works only included the effect of CMB energy density changes but neglected the change to the photon number density. We clearly define the dark photon distortion signal and show that in contrast to previous analytic estimates the distortion has an opposite sign and a $\simeq 1.5$ times larger amplitude. We furthermore extend the treatment into the large distortion regime to also cover the redshift range $\simeq 2\times 10^6-4\times 10^7$ between the $\mu$-era and the end of BBN using CosmoTherm. This shows that the CMB distortion constraints for dark photon masses in the range $10^{-4}\,{\rm eV}\lesssim m_{\rm dp}\lesssim 10^{-3}\,{\rm eV}$ were significantly underestimated. We demonstrate that in the small distortion regime the distortion caused by photon to dark photon conversion is extremely close to a $\mu$-type distortion independent of the conversion redshift. This opens the possibility to study dark photon models using CMB distortion anisotropies and the correlations with CMB temperature anisotropies as we highlight here., Comment: 13 pages, 10+2 figures, to be submitted to MNRAS, comments welcome

We consider theories which break the invariance under diffeomorphisms (Diff) down to transverse diffeomorphisms (TDiff) in the matter sector, consisting of multiple scalar fields. In particular, we regard shift-symmetric models with two free TDiff scalar fields in a flat Robertson-Walker spacetime and use the perfect fluid approach to study their dynamics. As a consequence of the symmetry breaking, an effective interaction between the fields is induced from the conservation of the total energy-momentum tensor, without the necessity to introduce any explicit interacting term in the Lagrangian. We study the different single-field domination regimes and analyze the energy exchange between the fields. Thereupon, we introduce an application of these models for the description of interactions in the dark sector, and compare the theoretical predictions of our model to observational data from Type Ia supernovae., Comment: 12 pages, 7 figures

Determining the Hubble constant (H0), a fundamental parameter describing cosmic expansion, remains a challenge due to conflicting measurements from the early and late universe. Gravitational wave (GW) observations from binary neutron star (BNS) mergers, with identified host galaxies through electromagnetic (EM) follow-up, offer an independent method to measure H0. However, this requires detection of numerous events, which could take decades with current GW detectors. LIGO-India can dramatically accelerate this effort. With sensitivity comparable to the existing LIGO detectors, its addition to the LIGO-Virgo network could increase detected events by 70%. This improvement nearly doubles when accounting for the detector's 70% duty cycle, increasing the probability of simultaneous operation of three detectors by a factor of ~2. We perform end-to-end simulations to estimate triple-coincidence detection rates and sky localization, considering realistic BNS populations, lightcurves, and EM observatory specifications. Our findings suggest LIGO-India could increase BNS events with observed kilonovae by ~2-7 times. The factor of few improvements in source localization precision with LIGO-India can allow much deeper EM follow-up campaigns (not considered in the simulations), potentially increasing the overall rate of detection of EM counterparts by a factor of ~20, which can have an enormous impact in addressing critical questions in different areas of astronomy. We evaluate the impact of LIGO-India in the context of H0 measurement and argue that it can cut down the required observation time of several decades by a factor of few and possibly to just few years with regular sensitivity upgrades., Comment: 18 pages, 7 figures

Ultra-light primordial black holes (PBHs) with masses $M_{\rm PBH}<5\times 10^8\mathrm{g}$ can dominate transiently the energy budget of the Universe and reheat the Universe through their evaporation taking place before Big Bang Nucleosynthesis. The isocurvature energy density fluctuations associated to the inhomogeneous distribution of a population of such PBHs can induce an abundant production of GWs due to second-order gravitational effects. In this work, we discuss the effect of primordial non-Gaussianity on the clustering properties of PBHs and study the effect of a clustered PBH population on the spectral shape of the aforementioned induced GW signal. In particular, focusing on local-type non-Gaussianity we find a double-peaked GW signal with the amplitude of the low-frequency peak being proportional to the square of the non-Gaussian parameter $\tau_\mathrm{NL}$. Remarkably, depending on the PBH mass $M_{\rm PBH}$ and the initial abundance of PBHs at formation time, i.e. $\Omega_\mathrm{PBH,f}$, this double-peaked GW signal can lie well within the frequency bands of forthcoming GW detectors, namely LISA, ET, SKA and BBO, hence rendering this signal falsifiable by GW experiments and promoting it as a novel portal probing the primordial non-Gaussianity., Comment: 19 pages plus appendices (32 pages in total), 2 figures

In the milli-Hertz frequency band, stochastic gravitational-wave background can be composed of both astronomical and cosmological sources, both can be anisotropic. Numerically depicting these anisotropies can be critical in revealing the underlying properties of their origins. For the first time, we perform a theoretical analysis of the constraining ability of TianQin on multiple moments of the stochastic background. First, we find that with a one-year operation, for a background with a signal-to-noise ratio of 16, TianQin can recover the multiple moments up to $l=4$. We also identified a unique feature of the stochastic background sky map, which is the mirror symmetry along the fixed orbital plane of TianQin. Thirdly, we explain the difference in anisotropy recovering ability between TianQin and LISA, by employing the criteria of the singularity of the covariance matrix (which is the condition number). Finally, we find that since the different data channel combinations correspond to different singularities, certain combinations might have an advantage in stochastic background map-making. We believe that the findings of this work can provide an important reference to future stochastic background analysis pipelines. It can also serve as a guideline for designing better gravitational-wave detectors aiming to decipher anisotropies in the stochastic background., Comment: 12 pages, 6 figures

In this article, we extend the standard $\Lambda$CDM model by incorporating causal viscous dark matter (vDM) modelled using Maxwell-Cattaneo theory and obtain a novel Hubble parameter solution for the model, which can even be extended to incorporate both radiation and baryonic matter components. A detailed and comprehensive analysis of the model is carried out by deriving theoretical constraints on model parameters, comparing the model with the latest observational data sets and validating the behaviour of the model under different thermodynamic laws. Such an in-depth analysis of the model yielded several intriguing results, like the presence of sign-switching bulk viscous pressure which aids both, the decelerated expansion in the early universe and the accelerated expansion in the late universe, possibility of having negative specific entropy rate in the early Universe while still satisfying the covariant second law of thermodynamics, and a correlation between relaxation time parameter and sign-switching redshift. Finally, we propose a unified dark matter (UDM) interpretation for the dark sector in this model and hence showed that, under the said UDM interpretation, this model can satisfy the much-required near equilibrium condition associated with the background dissipative theory both in the early and late phase of the Universe. Based on the NEC trend showcased by the model, we conjuncture that the late-accelerating behaviour of Universe can be viewed as a means for the UDM fluid to attain a global equilibrium state., Comment: 22 pages, 12 figures

A massive black hole can develop a dark-matter overdensity, and the dark matter changes the evolution of a stellar-mass compact object inspiraling around the massive black hole through the dense dark-matter environment. Specifically, dynamical friction speeds up the inspiral of the compact object and causes feedback on the dark-matter distribution. These intermediate mass-ratio inspirals with dark matter are a source of gravitational waves (GWs), and the waves can dephase significantly from an equivalent system in vacuum. Prior work has shown that this dephasing needs to be modeled to detect the GWs from these systems with LISA (the Laser Interferometer Space Antenna); it also showed that the density and distribution of dark matter can be inferred from a GW measurement. In this paper, we study whether the parametrized post-Einsteinian (ppE) framework can be used to infer the presence of dark matter in these systems. We confirm that if vacuum waveform templates are used to model the GWs from an inspiral in a dark-matter halo, then the resulting parameter estimation is biased. We then apply the ppE framework to determine whether it can reduce the parameter-estimation biases, and we find that adding one ppE phase term to a waveform template eliminates the parameter-estimation biases (statistical errors become larger than the systematic ones), but the effective post-Newtonian order in the ppE framework must be specified without uncertainties. When the post-Newtonian order has uncertainty, we find that the systematic errors on the ppE and the binary's parameters exceed the statistical errors. Thus, the simplest ppE framework would not give unbiased results for these systems, and a further extension of it, or dedicated parameter estimation with gravitational waveforms that include dark-matter effects would be needed., Comment: 16 pages, 8 figures

In this work we investigate the phenomenological implications of several non-trivial axion-Higgs couplings, which cover most of the possible non-perturbative scenarios. Specifically we consider the combination of having higher order non-renormalizable Higgs-axion couplings originating from a weakly coupled effective theory combined with non-perturbative couplings of the form $\sim \epsilon \Lambda_c^2|H|^2\cos (\frac{\phi}{f_a})$. Since we consider the misalignment axion, the non-perturbative couplings can be expanded in the form of a perturbation expansion in powers of $\phi/f_a$, thus after the electroweak symmetry breaking, the effective potential of the axion is drastically affected by these terms. We investigate the phenomenological implications of these terms for various values of the mass scale $\Lambda_c$, and some scenarios are theoretically disfavored, while other scenarios with non-perturbative Higgs-axion couplings of the form $\sim \epsilon \Lambda_c^2|H|^2\cos (\frac{\phi}{f_a})$ with $\Lambda_c\sim 10^{-10}\times m_a$ and $m_a\sim 10^{-10}\,$eV, lead to a characteristic pattern in the stochastic gravitational wave background via the deformation of the background equation of state parameter occurring at frequencies probed by the Einstein Telescope. We also consider loop effects from the Higgs sector caused by the term $\sim \epsilon \Lambda_c^2|H|^2\cos (\frac{\phi}{f_a})$ if we close the Higgs in one loop., Comment: PRD accepted

$f(R)$ theories of modified gravity may be compatible with current observations if the deviations from general relativity are sufficiently well screened in dense environments. In recent work [arXiv:2310.19955] we have shown that approximations commonly used to assess whether galaxies are screened, or unscreened, fail to hold in observationally interesting parts of parameter space. One of the assumptions commonly made in these approximations, and more broadly in the study of $f(R)$ models, is that the mass of the scalar mode can be neglected inside a galaxy. In this work we demonstrate that this approximation may fail spectacularly and discuss the implications of this for tests of the theory., Comment: 15 pages, 4 figures. Code available publicly at https://github.com/Bradley-March/scalar-compton-wavelength

A very pressing question in contemporary physics is the identity of Dark Matter (DM), and one that has not been answered affirmatively to any degree so far. Primordial Black Holes (PBHs) are one of the most well-motivated DM candidates. Light enough PBHs have been constrained by either the non-detection of their Hawking radiation itself, or by the non-observation of any measurable effects of this radiation on astrophysical and cosmological observables. We constrain the PBH density by their Hawking radiation effect on the intergalactic medium (IGM) temperature evolution. We use the latest deductions of IGM temperature from Lyman-$\alpha$ forest observations. We put constraints on the fraction of PBH DM with masses $5 \times 10^{15}$ g - $10^{17}$ g separately for spinning and non-spinning BHs. We derive constraints by dealing with the heating effects of the astrophysical reionization of the IGM in two ways. In one way, we completely neglect this heating due to astrophysical sources, thus giving us weaker constraints, but completely robust to the reionization history of the universe. In the second way, we utilise some modelling of the ionization and temperature history, and use it to derive more stringent constraints. We find that for non-spinning PBHs of mass $10^{16}$ g, the current measurements can constrain the PBH-density to be $\lesssim$ 0.1% of the total DM. We find that these constraints from the latest Lyman-$\alpha$ forest temperature measurements are competitive, and hence provide a new observable to probe the nature of PBH DM. The systematics affecting Lyman-$\alpha$ forest measurements are different from other constraining observations, and thus this is a complementary probe., Comment: v1; 15 pages, 2 Figures. Comments are welcome

Primordial gravitational waves could be non-Gaussian, just like primordial scalar perturbations. Although the tensor two-point function has thus-far remained elusive, the three-point function could, in principle, be large enough to be detected in Cosmic Microwave Background temperature and polarization anisotropies. We perform a detailed analysis of tensor and mixed tensor-scalar non-Gaussianity through the Planck PR4 bispectrum, placing constraints on eleven primordial templates, spanning various phenomenological and physical regimes including modifications to gravity, additional fields in inflation, and primordial magnetic fields. All analysis is performed using modern quasi-optimal binned estimators, and yields no evidence for tensor non-Gaussianity, with a maximum detection significance of $1.8\sigma$. Our constraints are derived primarily from large-scales (except for tensor-scalar-scalar models), and benefit greatly from the inclusion of $B$-modes. Although we find some loss of information from binning, mask effects and residual foreground contamination, our $f_{\rm NL}$ bounds improve over those of previous analyses by $40-600\%$, with six of the eleven models being analyzed for the first time. Unlike for scalar non-Gaussianity, future low-noise experiments such as LiteBIRD, the Simons Observatory and CMB-S4, will yield considerable improvement in tensor non-Gaussianity constraints., Comment: 23 pages, 6 figures, 3 tables, 0 detections. Submitted to Phys. Rev. D

We study conversion processes between gravitons and dark photons and reveal the effects of dark photons on the polarization of gravitational waves. Considering cosmological dark magnetic fields, we investigate the evolution of the intensity and polarization of gravitational waves through the conversion. Specifically, we demonstrate that for minimal coupling between gravitons and dark photons, the intensity, circular polarization, and linear polarization evolve separately. We derive explicit formulas for the statistical mean and variance of the intensity and polarization when the gravitational waves pass through magnetic fields with random orientation. The formulas capture how the initial polarization of dark photons will be imprinted on the observed gravitational wave background., Comment: 34 pages, 1 figure

We focus on the inflationary predictions of $\beta$-exponential potential models, in which the inflaton is a representation of the field delineating the size of extra-dimension. Since it offers a well-motivated starting point for the study of physics at very high energies, we incorporate an $R^2$ term in the Palatini gravity. In addition, afterward the inflation, the inflaton oscillates about the minimum of the inflation potential, and reheats the universe. This occurs during the reheating phase, at which the inflaton decays into the standard model particles, which fill the universe. We extend our examination by considering the reheating effects on inflationary observables by employing the different scenarios of the reheat temperature. Supposing the standard thermal history after inflation, we display the inflationary predictions, $n_s, r, \mathrm{d}n_s/\mathrm{d}\ln k$ of $\beta$-exponential potential with minimal coupling in Palatini $R^2$ gravity. Also, different kinds of constraints from a variety of observations, such as BICEP/Keck, Planck 2018, as well as future possible detectable sensitivities that might be reached by CMB experiments: CMB-S4 and LiteBIRD are taken into account in this work. We indicate that our results are consistent with both the latest data and the future sensitivity forecasts of LiteBIRD/Planck and CMB-S4. Finally, the results in this study highlight the viability of our model even in the case of the existence of more stringent constraints expected from future achievable confidence level limits., Comment: 1+32 pages, 12 figures, 1 table. Comments are welcome

Chern-Simons gravity is known to suffer from graviton ghost production during inflation, which suppresses the parity-violating power spectrum at scales relevant to cosmic microwave background observations. In this work, we show that allowing the initial conditions of inflation to deviate from the standard Bunch-Davies state can enhance parity-violating non-Gaussianity in the scalar-tensor cross-bispectra. Our results reveal a significant additional contribution to the cross-bispectra in the flattened configuration, offering a new avenue to constrain parity-violating gravity.

Bouncing cosmologies, while offering a compelling alternative to inflationary models, face challenges from the growth of vector perturbations during the contracting phase. While linear vector instabilities can be avoided with specific initial conditions or the absence of vector degrees of freedom, we demonstrate the significant role of secondary vector perturbations generated by non-linear interactions with scalar fluctuations. Our analysis reveals that in a broad class of single-field matter bounce scenarios, these secondary vector perturbations inevitably get unacceptably large amplitudes, provided the curvature fluctuations are consistent with cosmic microwave background observations. This finding underscores the crucial importance of scalar-induced vector perturbations in bouncing cosmology and highlights the need for further investigation into their potential impact on the viability of these models.

The symmetron is a light scalar which provides a screening mechanism so as to evade the strong constraints from local gravity tests. In order to achieve this goal, a $Z_2$ symmetry is imposed on the symmetron model. In this paper, we introduce a new symmetron Chern-Simons-like gravitational interaction which is $Z_2$ invariant but breaks the parity symmetry explicitly. As a result, it is found that this coupling can generate gravitational wave (GW) amplitude birefringence when GWs propagate over the symmetron backgrounds. Due to the matter density difference, the symmetron profile changes significantly when entering the galaxy, so that we need to discuss the extra-galactic and galactic situations separately. On the one hand, the cosmological symmetron field follows the adiabatic solution, which induces a parity-violating GW amplitude correction with its exponent proportional to the GW frequency and the traveling distance. On the other hand, the symmetron takes the screening solution within the Milky Way, and the generated GW birefringence is only a function of the GW frequency. By further comparing these two contributions, we find that the extra-galactic symmetron field produces the dominant birefringence effects. Finally, with the latest GW data from LIGO-Virgo-Kagra, we place a reasonable constraint on the parity-violating coupling parameter in this symmetron model., Comment: 22 pages

We consider the Kepler two-body problem in the presence of a cosmological constant Lambda. Several dimensionless parameters characterizing the possible orbit typologies are used to identify open and closed trajectories. The qualitative picture of the two-body motion is described and critical parameters of the problem are found., Comment: 21 pages, 9 figures

Recent advancements in gravitational wave astronomy hold the promise of a completely new way to explore our Universe. These lecture notes aim to provide a concise but self-contained introduction to key concepts of gravitational wave physics, with a focus on the opportunities to explore fundamental physics in transient gravitational wave signals and stochastic gravitational wave background searches.CERN-TH-2024-152, Comment: 31 pages, lecture notes prepared for TASI 2024 school. Comments welcome

In a recent paper: ``On the time dependency of $a_0$" the authors claim that they have tested ``one of the predictions of the Scale Invariant Vacuum (SIV) theory on MOND" by studying the dependence of the Modified Newtonian Dynamics (MOND) acceleration at two data sets, low-$z$ ($3.2\times10^{-4}\le z\le 3.2\times10^{-2}$) and high-$z$ ($0.5\le z\le 2.5$). They claim ``both samples show a dependency of $a_0$ from $z$". Here, the work mentioned above is revisited. The explicit analytic expression for the $z$-dependence of the $a_0$ within the SIV theory is given. Furthermore, the first estimates of the $\Omega_m$ within SIV theory give $\Omega_{m}=0.28\pm 0.04$ using the low-z data only, while a value of $\Omega_{m}=0.055$ is obtained using both data sets. This much lower $\Omega_m$ leaves no room for non-baryonic matter! Unlike in the mentioned paper above, the slope in the $z$-dependence of $A_0=\log_{10}(a_0)$ is estimated to be consistent with zero Z-slope for the two data sets. Finally, the statistics of the data are consistent with the SIV predictions; in particular, the possibility of change in the sign of the slopes for the two data sets is explainable within the SIV paradigm; however, the uncertainty in the data is too big for the clear demonstration of a $z$-dependence yet., Comment: 6 pages, 1 figure, to appear in a forthcoming MNRAS issue

An axion-like spectator during inflation can trigger a tachyonic instability which amplifies the modes of one of the helicities of the gauge field, resulting in the production of parity-violating gravitational waves (GWs). In this paper we investigate the impact of the coupling $RFF$ of the gauge field to gravity on the production of GWs. We find that such a coupling introduces a multiplicative factor to the tachyonic mass, which effectively enhances the amplitude of the gauge field modes. Produced GWs are expected to be observed by future space-based GW detectors. Additionally, we find that the strong backreaction due to particle production leads to multiple peaks in the energy spectrum of GWs., Comment: 8 pages, 3 figures

As a promising dark matter candidate, primordial black holes (PBHs) lighter than $\sim10^{-18}M_{\odot}$ are supposed to have evaporated by today through Hawking radiation. This scenario is challenged by the memory burden effect, which suggests that the evaporation of black holes may slow down significantly after they have emitted about half of their initial mass. We explore the astrophysical implications of the memory burden effect on the PBH abundance by today and the possibility for PBHs lighter than $\sim10^{-18}M_{\odot}$ to persist as dark matter. Our analysis utilizes current LIGO-Virgo-KAGRA data to constrain the primordial power spectrum and infer the PBH abundance. We find a null detection of scalar-induced gravitational waves that accompanied the formation of the PBHs. Then we find that PBHs are ruled out within the mass range $\sim[10^{-24},10^{-19}]M_{\odot}$. Furthermore, we expect that next-generation gravitational wave detectors, such as the Einstein Telescope and the Cosmic Explorer, will provide even more stringent constraints. Our results indicate that future detectors can reach sensitivities that could rule out PBH as dark matter within $\sim[10^{-29}M_{\odot},10^{-16}M_{\odot}]$ in the null detection of scalar-induced gravitational waves., Comment: 9 pages, 2 figures

In the summer of 2023, the pulsar timing arrays (PTAs) announced a compelling evidence for the existence of a nanohertz stochastic gravitational wave background (SGWB). Despite this breakthrough, however, several critical questions remain unanswered: What is the source of the signal? How can cosmic variance be accounted for? To what extent can we constrain nanohertz gravity? When will individual supermassive black hole binaries become observable? And how can we achieve a stronger detection? These open questions have spurred significant interests in PTA science, making this an opportune moment to revisit the astronomical and theoretical foundations of the field, as well as the data analysis techniques employed. In this review, we focus on the theoretical aspects of the SGWB as detected by PTAs. We provide a comprehensive derivation of the expected signal and its correlation, presented in a pedagogical manner, while also addressing current constraints. Looking ahead, we explore future milestones in the field, with detailed discussions on emerging theoretical considerations such as cosmic variance, the cumulants of the one- and two-point functions, subluminal gravitational waves, and the anisotropy and polarization of the SGWB., Comment: 31 pages + refs, 7 figures, invited chapter for `One Hundred and Ten Years of General Relativity -- From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity', v2: corrected typos, updated references

We investigate the first and second order cosmological perturbation equations in f(R) modified gravity theory and provide the equation of motion of second order scalar induced gravitational waves. We find that the effects of modified gravity not only change the form of the equation of motion of second order scalar induced gravitational waves but also contribute an additional anisotropic stress tensor, composed of first order scalar perturbations, to the source term of the gravitational waves. We calculate the energy density spectrum of second order scalar induced gravitational waves in the HS model. Utilizing current pulsar timing array observational data, we perform a rigorous Bayesian analysis of the parameter space of the HS model.

We consider a Bianchi I geometry of the Universe. We obtain a cosmic shear expression related with the eccentricity of the Universe. In particular we study the connection among cosmic shear, eccentricity and CMB. The equation are self-contained with only two parameters., Comment: 11 pages, accepted for publication on Universe

We found that, unlike General Relativity, the shift-symmetric subclass of Beyond Horndeski theories provides black holes with primary hair, which are thermodynamically stable and compatible with current Event Horizon Telescope observations for M87* and Sgr A* black holes. We first investigate its thermodynamic properties by studying the influence of the primary hair on the thermodynamic quantities and the local stability, imposing severe constraints in the allowed range of the primary hair values. Then, we analyze the null geodesics near this black hole, demonstrating how the scalar hair influences the shadow diameter, finding that higher values of the primary hair lead to smaller shadow sizes. Additionally, we constrain the scalar hair using the observational data, revealing its sensitivity to the choice of other black hole parameters. To further probe the observational features of the scalar hair, we simulate face-on two-dimensional images of spherically infalling accretion disks, examining how the primary scalar hair affects the black hole's shadow. Finally, we impose all relevant constraints to identify black holes that are both stable and consistent with observational data., Comment: 16 pages, 12 figures, 1 table

This work continues the research presented in the article [1], where we estimate the Gertsenshtein effect's influence on the long-wavelength part of relic gravitational wave spectrum. Here, the differential equation system for the Gertsenshtein effect in Friedman-LeMaitre-Robertson-Walker universe, derived in [1], is simplified for gravitational waves in the under-horizon regime during radiation dominance epoch. Then, the obtained system is solved analytically. As a result of the solution analysis a conclusion was made about a significant increase of relic GWs with the frequencies $ k\gtrsim 10^{-11}$ Hz for magnetic field strength about 1 nGs. In addition, at the end of the article model dependency of the result is discussed, Comment: 21 pages, 5 figures

We show that some holographic dark energy models can lead to a future evolution of the universe in which the scale factor $a$ is asymptotically constant, while $\dot a \rightarrow 0$ and the corresponding energy and pressure densities also vanish. We provide specific examples of such models and general conditions that can lead to an asymptotically static universe, which we have called the ``long freeze." We show that in some cases, such evolution can follow an arbitrarily long exponential expansion essentially identical to the asymptotic evolution of $\Lambda$CDM., Comment: 5 pages with no figures, comments very welcome !

The reconstruction of an inflationary universe considering the parametrization of the scalar spectral index as a function of the number of $e-$folds in the framework of a modified Friedmann equation is analyzed. In this context, we examine the possibility of reconstructing the Hubble parameter together with the effective potential considering a modified Friedmann equation specified by $\mathcal{F}(H)\propto \rho$, where $\mathcal{F}(H)$ corresponds to an arbitrary function of the Hubble parameter $H$ and $\rho$ denotes the energy density associated with the matter in the universe. To reconstruct the background variables during the inflationary scenario, we develop a new methodology by expressing the spectral index in terms of the Hubble parameter and its derivatives. Thus, we obtain a general formalism for the reconstruction of the inflation, using the slow roll approximation together with the parametrization of the scalar spectral index as a function of the number of $e-$folds $N$. As specific examples, we consider the simplest attractor $n_s-1=-2/N$ together with different functions $\mathcal{F}(H)$, associated to the modified Friedmann equation, to rebuild the Hubble parameter and the effective potential in terms of the scalar field $\phi$. Additionally, we examine the reheating epoch by considering a constant equation of state parameter, in which we determine the temperature and the number of e-folds during this epoch, using the background variables found during the reconstruction of the different $\mathcal{F}(H)-$models studied. Besides, we constrain the different parameters associated with the reconstructed inflationary $\mathcal{F}(H)-$models during the epochs of inflation and reheating, using current astronomical data from Planck and BICEP/Keck results., Comment: 25 pages and 9 figures

This study considers the specific case of a flat, minimally coupled to gravity, quintessence cosmology with a dark energy quartic polynomial potential that has the same mathematical form as the Higgs potential. Previous work on this case determined that the scalar field is given by a simple expression of the Lambert W function in terms of the easily observable scale factor. This expression provides analytic equations for the evolution of cosmological dark energy parameters as a function of the scale factor for all points on the Lambert W function principal branch. The Lambert W function is zero at a scale factor of zero that marks the big bang. The evolutionary equations beyond the big bang describe a canonical universe that is similar to {\Lambda}CDM, making it an excellent dynamical template to compare with observational data. The portion of the W function principal before the big bang extends to the infinite pre-bang past. It describes a noncanonical universe with an initially very low mass density that contracts by rolling down the dark energy potential to a singularity, big bang, at the scale factor zero point. This provides a natural origin for the big bang. It also raises the possibility that the universe existed before the big bang and is far older, and that it was once far larger than its current size. The recent increasing interest in the possibility of a dynamical universe instead of {\Lambda}CDM makes the exploration of the nature of such universes particularly relevant., Comment: 23 pages, 19 figures, Invited article for Universe Special Issue: Dark Energy and Dark Matter, Published September 5, 2024

Gravitational waves from cosmological phase transitions are novel probes of fundamental physics, making their precise calculation essential for revealing various mysteries of the early Universe. In this work we propose a framework that enables the consistent calculation of such gravitational waves sourced by sound waves. Starting from the Lagrangian, this framework integrates the calculation of the dynamics of first-order phase transitions in a self-consistent manner, eliminating various approximations typically introduced by conventional methods. At the heart of our approach is the congruous evaluation of the phase transition hydrodynamics that, at every step, is consistently informed by the Lagrangian. We demonstrate the application of our framework using the SM+$|H|^6$ model, deriving the corresponding gravitational wave spectrum. Our framework establishes a robust foundation for the precise prediction of gravitational waves from phase transitions., Comment: 8 pages, 4 figures, 1 table

Stage IV large scale structure surveys are promising probes of gravity on cosmological scales. Due to the vast model-space in the modified gravity literature, model-independent parameterisations represent useful and scalable ways to test extensions of $\Lambda$CDM. In this work we use a recently validated approach of computing the non-linear $3\times 2$pt observables in modified gravity models with a time-varying effective gravitational constant $\mu$ and a gravitational slip $\eta$ that is binned in redshift to produce Fisher forecasts for an LSST Y10-like survey. We also include in our modelling an effective nulling scheme for weak-lensing by applying the BNT transformation that localises the weak-lensing kernel enabling well-informed scale cuts. We show that the combination of improved non-linear modelling and better control of the scales that are modelled/cut yields high precision constraints on the cosmological and modified gravity parameters. We find that 4 redshift bins for $\mu$ of width corresponding to equal incremental $\Lambda$CDM growth is optimal given the state-of-the-art modelling and show how the BNT transformation can be used to mitigate the impact of small-scale systematic effects, such as baryonic feedback., Comment: 27 pages, 12 figures A few typos corrected and a couple of small changes made to the text to improve presentation of results, added missing reference. Comments welcome!

Massive black hole binary (MBHB) mergers will be detectable in large numbers by the Lisa Interferometer Space Antenna (LISA), which will thus provide new insights on how they form via repeated dark matter (DM) halo and galaxy mergers. Here we present a simple analytical model to generate a population of MBHB mergers based on a theoretical prescription that connects them to DM halo mergers. The high flexibility of our approach allows us to explore the broad and uncertain range of MBH seeding and growth mechanisms, as well as the different effects behind the interplay between MBH and galactic astrophysics. Such a flexibility is fundamental for the successful implementation and optimisation of the hierarchical Bayesian parameter estimation approach that here we apply to the MBHB population of LISA for the first time. Our inferred population hyper-parameters are chosen as proxies to characterise the MBH--DM halo mass scaling relation, the occupation fraction of MBHs in DM halos and the delay between halo and MBHB mergers. We find that LISA will provide tight constraints at the lower-end of the MBH-halo scaling relation, well complementing EM observations which are biased towards large masses. Furthermore, our results suggest that LISA will constrain some features of the MBH occupation fraction at high redshift, as well as merger time delays of the order of a few hundreds of Myr, opening the possibility to constrain dynamical evolution time scales such as the dynamical friction. The analysis presented here constitutes a first attempt at developing a hierarchical Bayesian inference approach to the LISA MBHB population, opening the way for several further improvements and investigations., Comment: 19 pages, 11 figures

We perform a study to obtain the initial spin or the nondimensional Kerr parameter $a_{*}$ of primordial black holes (PBHs) created during the radiation dominated phase of the universe from not only nearly monochromatic but also broad curvature power spectra. Motivated by inflation and first-order phase transitions, we consider a power law shape for the curvature perturbation. Although we can naturally neglect the contribution from the length scales smaller than the scale of interest, that from the larger scales may potentially be significant for a broad power spectrum, for which the spin is sensitive to the width of the power spectrum. So, we introduce a width parameter $r_{k}$, the ratio of the largest scale to the length of interest. We find that the root mean square of $a_{*}$ is largest for PBHs created from locally nearly scale invariant curvature power spectra with $r_{k} \sim 3.5$. The upper limit is $\sim 1\times 10^{-4}$ for $M=10^{17}-10^{23}$ g, $\sim 1.7\times 10^{-4}$ for $M=1-100 M_{\odot}$ and $\sim 2.5\times 10^{-3}$ even for an incredibly large mass of $M=10^{50}$ g., Comment: 17 pages, 5 figures

In the instant preheating scenario efficient particle production occurs immediately following the period of inflationary expansion in the early Universe. We demonstrate that instant preheating predicts unique gravitational wave (GW) signals arising from two distinct origins. One source is the bremsstrahlung GWs produced through the decay of superheavy particles, an inevitable consequence of instant preheating. The other is GWs generated from the nonlinear dynamics of the inflaton and coupled scalar fields. Using numerical simulations, we show that the peak of the GW spectrum shifts depending on the coupling constants of the theory. The detection of these dual GW signatures, characteristic of instant preheating, provides novel opportunities for probing the dynamics of the early Universe., Comment: 28 pages, 8 figures

We perform an observational study of modified gravity considering a potential inflationary interpretation of pulsar timing arrays (PTA). We use a motivated model known as no slip in which the gravitational wave propagation is modified. Specifically, by using two different parametrizations for the model, we find the approximate transfer functions for tensor perturbations. In this way, we obtain the spectral energy density of gravitational waves and use NANOGrav and IPTA second data release to constrain parameters of the model. We find that there is degeneracy between the model parameters $\xi$ and $c_M$. For $c_M$, we only get an upper bound on the parameter. Thus, it is difficult to constrain them with percent level accuracy with the current PTA data., Comment: 18 pages, 5 figures, 2 tables

We investigate the implications of memory burden on the gravitational wave (GW) spectrum arising from the Hawking evaporation of light primordial black holes (PBHs). By considering both rotating (Kerr) and non-rotating (Schwarzschild) PBHs, we demonstrate that the overproduction of primordial GWs from burdened PBHs could impose stringent constraints on the parameters governing backreaction effects. These constraints, derived from $\Delta N_{\rm eff}$ measurements by Planck and prospective experiments such as CMB-S4 and CMB-HD, offer novel insights into the impact of memory burden on PBH dynamics., Comment: 19 pages, 6 figures

We measure the speed of light with current observations, such as Type Ia Supernova, galaxy ages, radial BAO mode, as well as simulations of future redshift surveys and gravitational waves as standard sirens. By means of a Gaussian Process reconstruction, we find that the precision of such measurements can be improved from roughly 6\% to 1.5-2\%, in light of these forthcoming observations. This result demonstrates that we will be able to perform a cosmological measurement of a fundamental physical constant with unprecedented precision, which will help us underpinning if its value is truly consistent with local measurements, as predicted by the standard model of Cosmology., Comment: 12 pages, 1 appendix, 9 figures

In this work we revisit $\alpha$-Starobinsky inflation, also know as $E$-model, in the light of current CMB and LSS observations. The inflaton potential in the Einstein frame for this model contains a parameter $\alpha$ in the exponential, which alters the predictions for the scalar and tensor power spectra of Starobinsky inflation. We obtain these power spectra numerically without using slow-roll approximation and perform MCMC analysis to put constraints on parameters $M$ and $\alpha$ from Planck-2018, BICEP/Keck (BK18) and other LSS observations. We consider general reheating scenario by varying the number of e-foldings during inflation, $N_{pivot}$, along with the other parameters. We find $\log_{10}\alpha = 0.0^{+1.6}_{-5.6}$, $\log_{10}M= -4.91^{+0.69}_{-2.7}$ and $N_{pivot} = 53.2^{+3.9}_{-5}$ with $95\%$ C. L.. This implies that the present CMB and LSS observations are insufficient to constrain the parameter $\alpha$. We also find that there is no correlation between $N_{pivot}$ and $\alpha$., Comment: 15 pages, 5 figures

We propose a geometrical origin for the Shibata-Sasaki compaction function, which is known to be a reliable indicator of primordial black hole (PBH) formation, at least during radiation domination. We identify it with a compactness function in the static spacetime obtained by removing the cosmological scale factor from the metric in the long-wavelength limit. Furthermore, we discover that it reaches its maximum value of 1/2 at extremal surfaces on the constant-time spacelike hypersurface, which simultaneously are bifurcating trapping horizons and admit circular photon orbits in the static spacetime. Thus, the Shibata-Sasaki compaction function measures how close the positively curved region is to a type II configuration, with extremal surfaces where the value reaches 1/2., Comment: 13 pages, no figure

We investigate primordial magnetogenesis within a quantum bouncing model driven by a scalar field, focusing on various non-minimal couplings between the electromagnetic field and the scalar field. We test three cases: no coupling, a Cauchy coupling with gradual decay, and a Gaussian coupling with rapid fall-off. By exploring these scenarios, we assess a wide range of coupling strengths across different scales. The scalar field, with an exponential potential, behaves as pressureless matter in the asymptotic past of the contracting phase, as stiff matter around the bounce, and as dark energy during the expanding phase. Our findings reveal that, among the tested cases, only the Gaussian coupling can explain the generation of primordial magnetic fields on cosmological scales., Comment: 13 pages, 10 figures

In metric $f(R)$ gravity minimally coupled to the Standard Model, the scalaron could act as dark matter if its mass falls within the range $4.4~\text{meV} \lesssim m \lesssim 1.2~\text{MeV}$. The dynamics of the scalaron in the universe is influenced by the trace of the stress-energy tensor. In our previous studies, we focused on the classical contribution to this trace generated by the Higgs field. At the onset of the electroweak crossover, its evolution is nonadiabatic with respect to the scalaron mass, and the scalaron experiences a perturbation that can trigger its oscillations. However, the trace of the stress-energy tensor also includes a time-dependent component due to the QCD trace anomaly. In this paper, we revisit the cosmological scenario for scalaron evolution by incorporating the trace anomaly at high temperatures. We show that, while this anomaly produces a shift in the equilibrium value of the scalaron, the evolution of this shift remains adiabatic with respect to the rapid oscillations of the scalaron. Consequently, possible cosmological scenarios for the scalaron evolution are qualitatively unaffected by this correction., Comment: 12 pages

The dispersion measures of fast radio bursts have been identified as a powerful tool for testing the zero-mass hypothesis of the photon. The classical approach treats the massive photon-induced and plasma-induced time delays as two separate phenomena. Recently, Wang et al. (2024) suggested that the joint influence of the nonzero photon mass and plasma effects should be considered, and proposed a revised time delay for massive photons propagating in a plasma medium, denoted as $\Delta t'_{m_{\gamma}} \propto \nu^{-4}$, which departures from the classical dispersion relation ($\propto \nu^{-2}$). Here we discuss the derivation presented by Wang et al. (2024) and show that the classical dispersion relation remains valid based on Proca equations., Comment: 3 pages, 1 figure. Comment on arXiv:2403.06422. Accepted for publication in Research Notes of the AAS

Wave-optics phenomena in gravitational lensing occur when the signal's wavelength is commensurate to the gravitational radius of the lens. Although potentially detectable in lensed gravitational waves, fast radio bursts and pulsars, accurate numerical predictions are challenging to compute. Here we present novel methods for wave-optics lensing that allow the treatment of general lenses. In addition to a general algorithm, specialized methods optimize symmetric lenses (arbitrary number of images) and generic lenses in the single-image regime. We also develop approximations for simple lenses (point-like and singular isothermal sphere) that drastically outperform known solutions without compromising accuracy. These algorithms are implemented in Gravitational Lensing of Waves (GLoW): an accurate, flexible, and fast code. GLoW efficiently computes the frequency-dependent amplification factor for generic lens models and arbitrary impact parameters in O(1 ms) to O(10 ms) depending on the lens configuration and complexity. GLoW is readily applicable to model lensing diffraction on gravitational-wave signals, offering new means to investigate the distribution of dark-matter and large-scale structure with signals from ground and space detectors., Comment: 21 pages, 10 figures. GLoW is publicly available at https://github.com/miguelzuma/GLoW_public . All the scripts needed to reproduce the figures in this paper can also be found in the repository

In the single-field model, the preheating process occurs through self-resonance of inflaton field. We study the nonlinear structures generated during preheating in the $\alpha$-attractor models and monodromy models. The potentials have a power law form $\propto\left|\phi\right|^{2n}$ near the origin and a flat region away from bottom, which are consistent with current cosmological observations. The Floquet analysis shows that potential parameters in monodromy model have a significant influence on the region of resonance bands. The analytical oscillons solution for the $\alpha$-attractor T model with parameter $n=1$ is derived using the small amplitude analysis method. Besides we investigate the formation of nonlinear structures, the equation of state and the energy transfer through the (3+1) dimensional lattice simulation. We find that the symmetric T potential and the asymmetric E potential in the $\alpha$-attractor models have similar nonlinear dynamics. And the potential parameter $n$ in monodromy model significantly influences the lifetime of transients, whereas the parameter $q$ exerts minimal impact on the nonlinear dynamics., Comment: 14 pages, 12 figures, 2 tables

We put forward a primordial scenario to alleviate cosmological tensions, i.e. Hubble ($H_0$) tension and $ S_8 $ tension. Based on flat $\Lambda$CDM, the Bounce-Inflation (BI) scenario gives the results that $ H_0 = 68.60^{+0.40}_{-0.45} \, \text{km}/\text{s}/\text{Mpc}$, $ S_8 = 0.806 \pm 0.011 $ by using \texttt{Planck 2018} data sets and $ H_0 = 68.96 \pm 0.38 \, \text{km}/\text{s}/\text{Mpc}$, $ S_8 = 0.797\pm 0.010 $ by using \texttt{Planck 2018} + \texttt{SPT3G} data sets. These reduce the cosmological tensions slightly. We also take an extended $\Lambda$CDM model into account, $\Lambda$CDM (BI)+$A_L$, where $ A_L $ is the gravitational lensing amplitude. The results are $ H_0 = 69.38 \pm 0.49 \, \text{km}/\text{s}/\text{Mpc}$, $ S_8 = 0.774 \pm 0.014 $ fitted by \texttt{Planck 2018} data sets and $ H_0 = 69.49 \pm 0.45 \, \text{km}/\text{s}/\text{Mpc}$, $ S_8 = 0.771^{+0.013}_{-0.012} $ fitted by \texttt{Planck 2018} + \texttt{SPT3G} data sets, which reduce the Hubble tension to $\sim 3\sigma $ level and show no $S_8 $ tension. The $A_L \approx 1.1$ is smaller than the result of the inflation scenario with a constraint of \texttt{Planck 2018} data sets. Besides, the spectral index of the bounce-inflation scenario $ n_s $ is about $ 0.98 $, with a trend to the Harrison-Zel'dovich spectrum., Comment: 14 pages, 4 figures, 3 tables

Ultra-low mass primordial black holes (PBH), briefly dominating the expansion of the universe, would leave detectable imprints in the secondary stochastic gravitational wave background (SGWB). Such a scenario leads to a characteristic doubly peaked spectrum of SGWB and strongly depends on the Hawking evaporation of such light PBHs. However, these observable signatures are significantly altered if the memory burden effect during the evaporation of PBHs is taken into account. We show that for the SGWB induced by PBH density fluctuations, the memory burden effects on the Hawking evaporation of ultra-low mass PBHs can mimic the signal arising due to the non-standard reheating epoch before PBH domination. Finally, we point out that this degeneracy can be broken by the simultaneous detection of the first peak in the SGWB, which is typically induced by the inflationary adiabatic perturbations., Comment: 27 pages, 4 figures