Search

We study the dynamics of gauge-invariant scalar perturbations in cosmological scenarios with a modified Friedmann equation, such as quantum gravity bouncing cosmologies. We work within a separate universe approximation which captures wavelengths larger than the cosmological horizon; this approximation has been successfully applied to loop quantum cosmology and group field theory. We consider two variables commonly used to characterise scalar perturbations: the curvature perturbation on uniform-density hypersurfaces $\zeta$ and the comoving curvature perturbation $\mathcal{R}$. For standard cosmological models in general relativity as well as in loop quantum cosmology, these quantities are conserved and equal on super-horizon scales for adiabatic perturbations. Here we show that while these statements can be extended to a more general form of modified Friedmann equations similar to that of loop quantum cosmology, in other cases, such as the simplest group field theory bounce scenario, $\zeta$ is conserved across the bounce whereas $\mathcal{R}$ is not. We relate our results to approaches based on a second order equation for a single perturbation variable, such as the Mukhanov-Sasaki equation., Comment: 26 pages, 6 figures

Primordial non-Gaussianities from multi-field inflation are a leading target for cosmological observations, because of the possible large correlations generated between long and short distances. These signatures are captured by the local shape of the scalar bispectrum. In this paper, we revisit the nonlinearities of the conversion process from additional light scalars into curvature perturbations during inflation. We provide analytic templates for correlation functions valid at any kinematical configuration, using the cosmological bootstrap as a main computational tool. Our results include the possibility of large breaking of boost symmetry, in the form of small speeds of sound for both the inflaton and the mediators. We consider correlators coming from the tree-level exchange of a massless scalar field. By introducing a late-time cutoff, we identify that the symmetry constraints on the correlators are modified. This leads to anomalous conformal Ward identities, and consequently the bootstrap differential equations acquire a source term that depends on this cutoff. The solutions to the differential equations are scalar seed functions that incorporate these late-time growth effects. Applying weight-shifting operators to auxiliary "seed" functions, we obtain a systematic classification of shapes of non-Gaussianity coming from massless exchange. For theories with de Sitter symmetry, we compare the resulting shapes with the ones obtained via the $\delta N$ formalism, identifying missing contributions away from the squeezed limit. For boost-breaking scenarios, we derive a novel class of shape functions with phenomenologically distinct features. Specifically, the new shape provides a simple extension of equilateral non-Gaussianity: the signal peaks at a geometric configuration controlled by the ratio of the sound speeds of the mediator and the inflaton., Comment: 65 pages, 8 figures

This work presents a set of coupled Boltzmann equations describing the intensity and polarisation Stokes parameters of the SGWB. Collision terms, which account for gravitational Compton scattering off of massive objects, are also included. This set resembles that for the CMB Stokes parameters, but the different spin nature of the gravitational radiation and the physics involved in the scattering process determine crucial differences. In this case, due to the Rutherford angular dependence of the cross section, all the SGWB intensity multipoles of order $\ell$ are scattered out, producing outgoing intensity anisotropies of any order $\ell$ if they are present in the incoming radiation. On the other hand, SGWB linear polarisation modes can be expanded in a basis of spherical harmonics with $m=\pm 4$ and $\ell\ge 4$. This means that SGWB polarisation modes can be generated from unpolarised anisotropic radiation only with $m=\pm 4$, therefore requiring at least a hexadecapole anisotropy ($\ell\ge 4$) in the incoming intensity. Assuming a simplified toy model, we solve analytically the set of coupled Boltzmann equations to get explicit expressions for the intensity and polarisation angular power spectra. We confirm the contribution of the gravitational Compton scattering to the SGWB anisoptropies is extremely small for collisions with compact objects in the frequency range of current and upcoming surveys. The system of coupled Boltzmann equations presented here provides a way to an accurate estimate of the total amount of anisotropies generated by multiple SGWB scattering processes off of massive objects, as well as the interplay between polarisation and intensity, during the GW propagation across the LSS of the universe. These results will be useful for the full treatment of the astrophysical SWGB anisotropies in view of upcoming gravitational waves observatories., 28 pages, 2 tables, 2 figures. Matches the accepted version in JCAP

We analyze the physical content of squeezed bispectra involving long-wavelength tensor perturbations, showing that these modes cannot be gauged away, except for the exact (unphysical) limit of infinite wavelength, $k = 0$. This result has a direct implication on the validity of the Maldacena consistency relation, respected by a subclass of inflationary models. Consequently, in the squeezed limit, as in the case of the scalar-scalar-scalar bispectrum, squeezed mixed correlators could be observed by future experiments, remaining a key channel to study Early Universe physics and discriminate among different models of inflation., 13 pages

Journal of cosmology and astroparticle physics 01(01), 009 (2023). doi:10.1088/1475-7516/2023/01/009, We show that very compact axion mini-clusters can form in models where axion-like-particle (ALP) dark matter is produced via the kinetic misalignment mechanism, which is well-motivated in pre-inflationary $U(1)$ symmetry breaking scenarios. This is due to ALP fragmentation. We predict denser halos than what has been obtained so far in the literature from standard misalignment in post-inflationary $U(1)$ breaking scenarios or from large misalignment. The main reason is that adiabatic fluctuations are significant at early times; therefore, even if amplification from parametric resonance effects is moderate, the final size of ALP fluctuations is larger in kinetic misalignment. We compare halo mass functions and halo spectra obtained in kinetic misalignment, large misalignment, and standard misalignment, respectively. Our analysis does not depend on the specific model realization of the kinetic misalignment mechanism. We present our results generally as a function of the ALP mass and the ALP decay constant only. We show that a sizable region of this ALP parameter space can be tested by future experiments that probe small-scale structures., Published by IOP, London

Diverse astrophysical observations suggest the existence of cold dark matter that interacts only gravitationally with radiation and ordinary baryonic matter. Any nonzero coupling between dark matter and baryons would provide a significant step towards understanding the particle nature of dark matter. Measurements of the cosmic microwave background (CMB) provide constraints on such a coupling that complement laboratory searches. In this work we place upper limits on a variety of models for dark matter elastic scattering with protons and electrons by combining large-scale CMB data from the Planck satellite with small-scale information from Atacama Cosmology Telescope (ACT) DR4 data. In the case of velocity-independent scattering, we obtain bounds on the interaction cross section for protons that are 40\% tighter than previous constraints from the CMB anisotropy. For some models with velocity-dependent scattering we find best-fitting cross sections with a 2$\sigma$ deviation from zero, but these scattering models are not statistically preferred over $\Lambda$CDM in terms of model selection., Comment: 8 pages, 4 figures

We consider the possibility of extra spinning particles during inflation, focussing on the spin-2 case. Our analysis relies on the well-known fully non-linear formulation of interacting spin-2 theories. We explore the parameter space of the corresponding inflationary Lagrangian and identify regions therein exhibiting signatures within reach of upcoming CMB probes. We provide a thorough study of the early and late-time dynamics ensuring that stability conditions are met throughout the cosmic evolution. We characterise in particular the gravitational wave spectrum and three-point function finding a local-type non-Gaussianity whose amplitude may be within the sensitivity range of both the LiteBIRD and CMB-S4 experiments., 30 pages, 6 figures; v2 -- references added, minor changes, accepted for publication in JCAP

We examine the possibility of "soft cosmology", namely small deviations from the usual framework due to the effective appearance of soft-matter properties in the Universe sectors. One effect of such a case would be the dark energy to exhibit a different equation-of-state parameter at large scales (which determine the universe expansion) and at intermediate scales (which determine the sub-horizon clustering and the large scale structure formation). Concerning soft dark matter, we show that it can effectively arise due to the dark-energy clustering, even if dark energy is not soft. We propose a novel parametrization introducing the "softness parameters" of the dark sectors. As we see, although the background evolution remains unaffected, due to the extreme sensitivity and significant effects on the global properties even a slightly non-trivial softness parameter can improve the clustering behavior and alleviate e.g. the $f\sigma_8$ tension. Lastly, an extension of the cosmological perturbation theory and a detailed statistical mechanical analysis, in order to incorporate complexity and estimate the scale-dependent behavior from first principles, is necessary and would provide a robust argumentation in favour of soft cosmology., Comment: 5 pages, 2 figures

We consider the entropy associated with the large-scale structure of the Universe in the linear regime, where the Universe can be described by a perturbed Friedmann-Lema\^itre spacetime. In particular, we compare two different definitions proposed in the literature for the entropy using a spatial averaging prescription. For one definition, the entropy of the large-scale structure for a given comoving volume always grows with time, both for a CDM and a $\Lambda$CDM model. In particular, while it diverges for a CDM model, it saturates to a constant value in the presence of a cosmological constant. The use of a light-cone averaging prescription in the context of the evaluation of the entropy is also discussed., Comment: 10 pages, 4 figures. Presentation improved, typos corrected, previous subsection III.B merged with subsection II.C, comments, clarifications and a reference added. Version accepted for publication in GRG

Decaying dark matter models provide a physically motivated way of channeling energy between the matter and radiation sectors. In principle, this could affect the predicted value of the Hubble constant in such a way as to accommodate the discrepancies between CMB inferences and local measurements of the same. Here, we revisit the model of warm dark matter decaying non-relativistically to invisible radiation. In particular, we rederive the background and perturbation equations starting from a decaying neutrino model and describe a new, computationally efficient method of computing the decay product perturbations up to large multipoles. We conduct MCMC analyses to constrain all three model parameters, for the first time including the mass of the decaying species, and assess the ability of the model to alleviate the Hubble and $\sigma_8$ tensions, the latter being the discrepancy between the CMB and weak gravitational lensing constraints on the amplitude of matter fluctuations on an $8 h^{-1}$ Mpc$^{-1}$ scale. We find that the model reduces the $H_0$ tension from $\sim 4 \sigma$ to $\sim 3 \sigma$ and neither alleviates nor worsens the $S_8 \equiv \sigma_8 (\Omega_m/0.3)^{0.5}$ tension, ultimately showing only mild improvements with respect to $\Lambda$CDM. However, the values of the model-specific parameters favoured by data is found to be well within the regime of relativistic decays where inverse processes are important, rendering a conclusive evaluation of the decaying warm dark matter model open to future work., Comment: 41 pages (main text 25 pages), 16 figures; v2: minor corrections, submitted to JCAP

In a previous paper (P. D. Mannheim, Phys. Rev. D 102, 123535 (2020)) we studied cosmological perturbation theory in the cosmology associated with the fourth-order derivative conformal gravity theory, and provided an exact solution to the theory in the recombination era. In this paper we present an exact solution that holds all the way from recombination until the current era., Comment: 23 pages. arXiv admin note: substantial text overlap with arXiv:2009.06841

We apply the "systematic" $1^{st}$ order cosmological perturbation theory method to re-derive the formulation of an inflationary model generated by variation of constants, then to study the case where it is non-minimally coupled to gravity within both the "Metric" and "Palatini" formulations. Accommodating Planck 2018 data with a length scale $\ell$ larger than Planck Length $L_{pl}$ requires amending the model. First, we assume $f(R)$ gravity where we show that an $R^2$-term within Palatini formulation is able to make the model viable. All along the discussions, we elucidate the origin of the difference between the "Metric" and "Palatini" formalisms, and also highlight the terms dropped when applying the shortcut "potential formulae method", unlike the "systematic' method", for the observable parameters. Second, another variant of the model, represented by a two-exponentials potential, fits also the data with $\ell> L_{pl}$., 16 pages, 3 figures. Major revision. Version to appear in IJMPA

Analytical computations in relativistic cosmology can be split into two sets: time evolution relating the initial conditions to the observer's light-cone and light propagation to obtain observables. Cosmological perturbation theory in the FLRW coordinates constitutes an efficient tool for the former task, but the latter is dramatically simpler in light-cone-adapted coordinates that trivialize the light rays towards the observer world-line. Here we point out that time evolution and observable reconstruction can be combined into a single computation that relates directly initial conditions to observables. This is possible if one works uniquely in such light-cone coordinates, thus completely bypassing the FLRW "middle-man" coordinates. We first present in detail these light-cone coordinates, extending and generalizing the presently available material in the literature, and construct a particularly convenient subset for cosmological perturbation theory. We then express the Einstein and energy-momentum conservation equations in these coordinates at the fully non-linear level. This is achieved through a careful 2+1+1 decomposition which leads to relatively compact expressions and provides good control over the geometrical interpretation of the involved quantities. Finally, we consider cosmological perturbation theory to linear order, paying attention to the remaining gauge symmetries and consistently obtaining gauge-invariant equations. Moreover, we show that it is possible to implement statistical homogeneity on stochastic fluctuations, despite the fact that the coordinate system privileges the observer world-line., 43 pages

The massive neutrinos of the Cosmic Neutrino Background (CνB) are fundamental ingredients of the radiation-dominated early universe and are important non-relativistic probes of the large-scale structure formation in the late universe. The dominant source of anisotropies in the neutrino flux distribution on the sky are highly amplified integrals of metric perturbations encountered during the non-relativistic phase of the CνB. This paper numerically compares the line-of-sight methods for computing CνB anisotropies with the Einstein-Boltzmann hierarchy solutions in linear theory for a range of neutrino masses. Angular power spectra are computed that are relevant to a future polarized tritium target run of the PTOLEMY experiment. Correlations between the CνB sky maps and galactic survey data are derived using line-of-sight techniques and discussed in the context of multi-messenger astrophysics.

The impact of dark matter-neutrino interactions on the measurement of the cosmological parameters has been investigated in the past in the context of massless neutrinos exclusively. Here we revisit the role of a neutrino-dark matter coupling in light of ongoing cosmological tensions by implementing the full Boltzmann hierarchy for three massive neutrinos. Our tightest 95% CL upper limit on the strength of the interactions, parameterized via $u_\chi =\frac{\sigma_0}{\sigma_{Th}}\left(\frac{m_\chi}{100 \text{GeV}}\right)^{-1}$, is $u_\chi\leq3.34 \cdot 10^{-4}$, arising from a combination of Planck TTTEEE data, Planck lensing data and SDSS BAO data. This upper bound is, as expected, slightly higher than previous results for interacting massless neutrinos, due to the correction factor associated with neutrino masses. We find that these interactions significantly relax the lower bounds on the value of $\sigma_8$ that is inferred in the context of $\Lambda$CDM from the Planck data, leading to agreement within 1-2$\sigma$ with weak lensing estimates of $\sigma_8$, as those from KiDS-1000. However, the presence of these interactions barely affects the value of the Hubble constant $H_0$., Comment: 31 pages, 8 figures, 3 tables

Up-to-date cosmological data analyses have shown that \textit{(a)} a closed universe is preferred by the Planck data at more than $99\%$ CL, and \textit{(b)} interacting scenarios offer a very compelling solution to the Hubble constant tension. In light of these two recent appealing scenarios, we consider here an interacting dark matter-dark energy model with a non-zero spatial curvature component and a freely varying dark energy equation of state in both the quintessential and phantom regimes. When considering Cosmic Microwave Background data only, a phantom and closed universe can perfectly alleviate the Hubble tension, without the necessity of a coupling among the dark sectors. Accounting for other possible cosmological observations compromises the viability of this very attractive scenario as a global solution to current cosmological tensions, either by spoiling its effectiveness concerning the $H_0$ problem, as in the case of Supernovae Ia data, or by introducing a strong disagreement in the preferred value of the spatial curvature, as in the case of Baryon Acoustic Oscillations., Revised version; 12 pages, 2 figures and 7 tables; published version in JCAP

In this article, we study in detail the linear dynamics and cubic interactions for any number $N_\mathrm{field}$ of scalar fields during inflation, directly in terms of the observable curvature perturbation $\zeta$ and $N_\mathrm{field}-1$ entropic fluctuations, a choice that is more suitable for analytical works. In the linear equations of motion for the perturbations, we uncover rich geometrical effects beyond terms involving just the scalar curvature of the field space, and that come from the non-canonical kinetic structure of the scalar fields when the dimension of the field space is larger than two. Moreover, we show that a fast rotation of the local entropic basis can result in negative eigenvalues for the entropic mass matrix, potentially destabilising the background dynamics when $N_\mathrm{field} \geqslant 3$. We also explain how to render manifest the sizes of cubic interactions between the adiabatic and the entropic fluctuations, extending a previous work of ours to any number of interacting fields. As a first analytical application of our generic formalism, we derive the effective single-field theory for perturbations up to cubic order when all entropic fluctuations are heavy enough to be integrated out. In a slow-varying limit, we recover the cubic action expected from the effective field theory of inflation, but with a prediction for the usual Wilson coefficients in terms of the multifield parameters, thus proposing a new interpretation of the bispectrum in this generic $N_\mathrm{field}$ context., Comment: 30 pages, 1 figure

Galaxy imaging surveys provide us with information on both the galaxy distribution and their shapes. In this paper, we systematically investigate the sensitivity of galaxy shapes to new physics in the initial conditions. For this purpose, we decompose the galaxy shape function into spin components, and compute the contributions to each spin component from both intrinsic alignment and weak lensing. We then consider the angular-dependent primordial non-Gaussianity, which is generated by a non-zero integer spin particle when active during inflation, and show that a galaxy imaging survey essentially functions as a spin-sensitive detector of such particles in the early universe. We also perform a forecast of the PNG generated from a higher spin particle, considering a Rubin Observatory LSST-like galaxy survey., 50 pages, 8 figures

In this paper, we use a complete model of classical primordial standard clocks as an example to develop a methodology of directly comparing numerical predictions from complicated multi-field feature models with the Planck data, including the Planck 2018 Plik unbinned likelihood and the statistically most powerful CamSpec 2020 likelihood for temperature and polarization data. As this two-field inflationary model offers a plethora of primordial feature spectra that represent combinations of sharp and resonance feature signals non-trivially distributed over extended cosmological scales, its data comparison has not been satisfactorily addressed by previous attempts using analytical templates. The method of this paper, consisting of numerical prediction, effective parameter construction and nested sampling data comparison, allows us to efficiently explore every possible spectra from the model. We classify the resulting feature candidates in three different frequency ranges. We use the Bayesian evidences to assess the statistical significance of the candidates over the baseline model, taking into account the effect of additional parameters and the look-elsewhere effect. Although none of the candidates is statistically significant, the methodology of this paper can be used to facilitate the future model-building and data-screening process of primordial features, and the candidates can be subjected to further tests with data from the upcoming cosmic microwave background polarization observations and galaxy surveys., Comment: v1: 37 pages, 19 figures and 3 tables; v2: references added, accepted for publication in JCAP

We compute the inflationary perturbation spectra and the quantity $r+8n_{T}$ to the next-to-next-to-leading log order in quantum gravity with purely virtual particles (which means the theory $R+R^{2}+C^{2}$ with the fakeon prescription/projection for $C^{2}$). The spectra are functions of the inflationary running coupling $\alpha (1/k)$ and satisfy the cosmic renormalization-group flow equations, which determine the tilts and the running coefficients. The tensor fluctuations receive contributions from the spin-2 fakeon $\chi_{\mu \nu }$ at every order of the expansion in powers of $\alpha \sim 1/115$. The dependence of the scalar spectrum on the $\chi_{\mu \nu }$ mass $m_{\chi }$, on the other hand, starts from the $\alpha ^{2}$ corrections, which are handled perturbatively in the ratio $m_{\phi }/m_{\chi }$, where $m_{\phi }$ is the inflaton mass. The predictions have theoretical errors ranging from $\alpha ^{4}\sim 10^{-8}$ to $\alpha ^{3}\sim 10^{-6}$. Nontrivial issues concerning the fakeon projection at higher orders are addressed., Comment: 28 pages; JCAP

The large enhancement of the primordial power spectrum of the curvature perturbation can seed the formation of primordial black hole, that can play as a dark matter component in the Universe. In multi-filed inflation models, the curved trajectory of the scalar fields in the field space can generate a peak in the power spectrum on small scales due to the existence of the isocurvature perturbation. Here we show that a potential can be reconstructed from a given power spectrum, which is made of a scale-invariant one on large scales and the other function with a peak on small scales. In multi-field inflation models the reconstructed potential may not be unique and we can find different potentials from a given power spectrum., Comment: 14 pages, 4 figures

The linearized dynamical equation for metric perturbations in a fully general, non-vacuum, background geometry is obtained from the Hamilton variational principle applied to the action up to second order. We specialize our results to the case of traceless and transverse metric fluctuations, and we discuss how the intrinsic properties of the matter stress tensor can affect (and modify) the process of gravity wave propagation even in most conventional geometric scenarios, like (for instance) those described by a FLRW metric background. We provide explicit examples for fluid, scalar field and electromagnetic field sources., Comment: 17 pages, no figures

The robustness of multi-field inflation to the physics of reheating is investigated. In order to carry out this study, reheating is described in detail by means of a formalism which tracks the evolution of scalar fields and perfect fluids in interaction (the inflatons and their decay products). This framework is then used to establish the general equations of motion of the background and perturbative quantities controlling the evolution of the system during reheating. Next, these equations are solved exactly by means of a new numerical code. Moreover, new analytical techniques, allowing us to interpret and approximate these solutions, are developed. As an illustration of a physical prediction that could be affected by the micro-physics of reheating, the amplitude of non-adiabatic perturbations in double inflation is considered. It is found that ignoring the fine-structure of reheating, as usually done in the standard approach, can lead to differences as big as $\sim 50\%$, while our semi-analytic estimates can reduce this error to $\sim 10\%$. We conclude that, in multi-field inflation, tracking the perturbations through the details of the reheating process is important and, to achieve good precision, requires the use of numerical calculations., 80 pages + appendices

The separate-universe approach provides an effective description of cosmological perturbations at large scales, where the universe can be described by an ensemble of independent, locally homogeneous and isotropic patches. By reducing the phase space to homogeneous and isotropic degrees of freedom, it greatly simplifies the analysis of large-scale fluctuations. It is also a prerequisite for the stochastic-inflation formalism. In this work, we formulate the separate-universe approach in the Hamiltonian formalism, which allows us to analyse the full phase-space structure of the perturbations. Such a phase-space description is indeed required in dynamical regimes which do not benefit from a background attractor, as well as to investigate quantum properties of cosmological perturbations. We find that the separate-universe approach always succeeds in reproducing the same phase-space dynamics for homogeneous and isotropic degrees of freedom as the full cosmological perturbation theory, provided that the wavelength of the modes under consideration are larger than some lower bound that we derive. We also compare the separate-universe approach and cosmological perturbation theory at the level of the gauge-matching procedure, where the agreement is not always guaranteed and requires specific matching prescriptions that we present., Comment: Discussion around equation (4.12) expanded, few minor changes (main conclusions unchanged)

We study the evolution of cosmological perturbations in dark-matter models with elastic and velocity-independent self interactions. Such interactions are imprinted in the matter-power spectrum as dark acoustic oscillations, which can be experimentally explored to determine the strength of the self scatterings. Models with self interactions have similarities to warm dark matter, as they lead to suppression of power on small scales when the dark-matter velocity dispersion is sizable. Nonetheless, both the physical origin and the extent of the suppression differ for self-interacting dark matter from conventional warm dark matter, with a dark sound horizon controlling the reduction of power in the former case, and a free-streaming length in the latter. We thoroughly analyze these differences by performing computations of the linear power spectrum using a newly developed Boltzmann code. We find that while current Lyman-$\alpha$ data disfavor conventional warm dark matter with a mass less than 5.3 keV, when self interactions are included at their maximal value consistent with bounds from the Bullet Cluster, the limits are relaxed to 4.4 keV. Finally, we make use of our analysis to set novel bounds on light scalar singlet dark matter., Comment: 30 pages, 7 figures, 5 appendices

By a careful implementation of gauge transformations involving long-wavelength modes, we show that a variety of effects involving squeezed bispectrum configurations, for which one Fourier mode is much shorter than the other two, cannot be gauged away, except for the unphysical exactly infinite-wavelength ($k=0$) limit. Our result applies, in particular, to the Maldacena consistency relation for single-field inflation, yielding a local non-Gaussianity strength $f_{\rm NL}^{\rm local} = - (5/12)(n_S-1)$ (with $n_S$ the primordial spectral index of scalar perturbations), and to the $f_{\rm NL}^{\rm GR} = -5/3$ term, appearing in the dark matter bispectrum and in the halo bias, as a consequence of the general relativistic non-linear evolution of matter perturbations. Such effects are therefore physical and observable in principle by future high-sensitivity experiments., 19 pages, no figures. LaTex. Version accepted for publication in JCAP, minor changes

The galaxy number density is a key quantity to compare theoretical predictions to the observational data from current and future Large Scale Structure surveys. The precision demanded by these Stage IV surveys requires the use of second order cosmological perturbation theory. Based on the independent calculation published previously, we present the result of the comparison with the results of three other groups at leading order. Overall we find that the differences between the different approaches lie mostly on the definition of certain quantities, where the ambiguity of signs results in the addition of extra terms at second order in perturbation theory., V2: 10 pages. Version accepted for publication in CQG

The primordial magnetic fields (PMFs) produced in the early universe are expected to be the origin of the large-scale cosmic magnetic fields. The PMFs are considered to leave a footprint on the cosmic microwave background (CMB) anisotropies due to both the electromagnetic force and gravitational interaction. In this paper, we investigate how the PMFs affect the CMB anisotropies on smaller scales than the mean-free-path of the CMB photons. We solve the baryon Euler equation with Lorentz force due to the PMFs, and we show that the vector-type perturbations from the PMFs induce the CMB anisotropies below the Silk scale as $\ell>3000$. Based on our calculations, we put a constraint on the PMFs from the combined CMB temperature anisotropies obtained by Planck and South Pole Telescope (SPT). We have found that the highly-resolved temperature anisotropies of the SPT 2017 bandpowers at $\ell \lesssim 8000$ favor the PMF model with a small scale-dependence. As a result, the Planck and SPT's joint-analysis puts a constraint on the PMF spectral index as $n_B, Comment: 18 pages, 5 figures, 1 table, published in JCAP

We calculate the gravitational waves (GWs) induced by the density fluctuations due to inhomogeneous distribution of primordial black holes (PBHs) in the case where PBHs eventually dominate and reheat the universe by Hawking evaporation. The initial PBH density fluctuations are isocurvature in nature. We find that most of the induced GWs are generated right after evaporation, when the universe transits from the PBH dominated era to the radiation dominated era and the curvature perturbation starts to oscillate wildly. The strongest constraint on the amount of the produced GWs comes from the big bang nucleosynthesis (BBN). We improve previous constraints on the PBH fraction and find that it cannot exceed $10^{-3}$. Furthermore, this maximum fraction decreases as the mass increases and reaches $10^{-9}$ for $M_{\rm PBH}\sim 5\times10^8 {\rm g}$, which is the largest mass allowed by the BBN constraint on the reheating temperature. Considering that PBH may cluster above a given clustering scale, we also derive a lower bound on the scale of clustering. Interestingly, the GW spectrum for $M_{\rm PBH}\sim 10^4 -10^8 {\rm g}$ enters the observational window of LIGO and DECIGO and could be tested in the future. Although we focus on the PBH dominated early universe in this paper, our methodology is applicable to any model with early isocurvature perturbation., Revised version. Included suppression due to the finite duration of black hole evaporation

We present a detailed comparison of the newly developed particle-based Kinetic Field Theory framework for cosmic large-scale structure formation with the established formalism of Eulerian Standard Perturbation Theory. We highlight the qualitative differences of both approaches by a comparative analysis of the respective equations of motion and implementation of initial conditions. A natural starting point for a first quantitative comparison is given by the non-interacting regime of free-streaming kinematics. Our results suggest that Kinetic Field Theory contains a complete resummation of Standard Perturbation Theory in this regime. We further show that the exact free-streaming solution of Kinetic Field Theory cannot be recovered in any finite order of Standard Perturbation Theory. Kinetic Field Theory should therefore provide a better starting point for perturbative treatments of non-linear structure formation.

A logarithm transformation over the matter overdensity field $\delta$ brings information from the bispectrum and higher-order n-point functions to the power spectrum. We calculate the power spectrum for the log-transformed field $A$ at one, two and three loops using perturbation theory (PT). We compare the results to simulated data and give evidence that the PT series is asymptotic already on large scales, where the $k$ modes no longer decouple. This motivates us to build an alternative perturbative series for the log-transformed field that is not constructed on top of perturbations of $\delta$ but directly over the equations of motion for $A$ itself. This new approach converges faster and better reproduces the large scales at low $z$. We then show that the large-scale behaviour for the log-transformed field power spectrum can be captured by a small number of free parameters. Finally, we add the counter-terms expected within the effective field theory framework and show that the theoretical model, together with the IR-resummation procedure, agrees with the measured spectrum with percent precision until $k \simeq 0.38 $ Mpc$^{-1}$h at $z=0$. It indicates that the non-linear transformation indeed linearizes the density field and, in principle, allows us to access information contained on smaller scales., Comment: 32 pages, 11 figures. Comments are welcome. (v2: extra figure and a few changes after going through the refereeing process of JCAP)

We study one-loop corrections to the two-point correlation function of tensor perturbations in primordial cosmology induced by massless spectator matter fields. Using the Schwinger-Keldysh formalism in cosmological perturbation theory, we employ dimensional regularization and cutoff regularization to study the finite quantum corrections at one-loop arising from isocurvature fields of the massless scalar, fermion and abelian gauge field which are freely propagating on the FRW spacetime. For all cases, we find a logarithmic running of the form $\frac{C}{q^3} \, \frac{H^4}{M^4_p} \log \left( \frac{H}{\mu } \right)$ where $C$ is a negative constant related to the beta function, $H$ is the Hubble parameter at horizon exit and $\mu$ is the renormalization scale., Comment: 33 pages, 2 figures: improved discussion of the covariant cutoff regularization method, some reorganization of materials, references added

Delta-gravity (DG) is a gravitational model based on an extension of general relativity given by a new symmetry called . In this model, new matter fields are added to the original matter fields, motivated by the additional symmetry. We call them matter fields. This model predicts an accelerating universe without the need to introduce a cosmological constant. In this work, we study the scalar cosmic microwave background (CMB) temperature (TT) power spectrum predicted by DG using an analytical hydrodynamic approach. To fit the Planck satellite’s data with the DG model, we used a Markov Chain Monte Carlo analysis. We also include a study about the compatibility between Type Ia supernovae (SNe Ia) and CMB observations in the DG context. Finally, we obtain the scalar CMB TT power spectrum and the fitted parameters needed to explain both SN Ia data and CMB measurements. The results are in reasonable agreement with both observations considering the analytical approximation. We also discuss whether the Hubble constant and the accelerating universe are in concordance with the observational evidence in the DG context.

A stealth de Sitter solution in scalar-tensor theories has an exact de Sitter background metric and a nontrivial scalar field profile. Recently, in the context of Degenerate Higher-Order Scalar-Tensor (DHOST) theories it was shown that stealth de Sitter solutions suffer from either infinite strong coupling or gradient instability for scalar field perturbations. The sound speed squared is either vanishing or negative. In the first case, the strong coupling scale is zero and thus lower than the energy scale of any physical phenomena. From the viewpoint of effective field theory, this issue is naturally resolved by introducing a controlled detuning of the degeneracy condition dubbed scordatura, recovering a version of ghost condensation. In this paper we construct a viable dark energy model in the scordatura DHOST theory based on a stealth cosmological solution, in which the metric is the same as in the standard $\Lambda$CDM model and the scalar field profile is linearly time-dependent. We show that the scordatura mechanism resolves the strong coupling and gradient instability. Further, we find that the scordatura is also necessary to make the quasi-static limit well-defined, which implies that the subhorizon observables are inevitably affected by the scordatura. We derive the effective gravitational coupling and the correction to the friction term for the subhorizon evolution of the linear dark matter energy density contrast as well as the Weyl potential and the gravitational slip parameter. In the absence of the scordatura, the quasi-static approximation would break down at all scales around stealth cosmological solutions even if the issue of the infinite strong coupling is unjustly disregarded. Therefore previous estimations of the subhorizon evolution of matter density contrast in modified gravity in the literature need to be revisited by taking into account the scordatura effect., Comment: 33 pages, typos corrected, published version

We provide a general framework for self-interacting warm dark matter (WDM) in cosmological perturbations, by deriving from first principles a Boltzmann hierarchy which retains certain independence from a particular interaction Lagrangian. We consider elastic interactions among the massive particles, and obtain a hierarchy which is more general than the ones usually obtained for non-relativistic (as for cold DM) or for ultra-relativistic (as for neutrinos) approximations. The more general momentum-dependent kernel integrals in the Boltzmann collision terms, are explicitly calculated for different field-mediator models, including examples of a scalar field (either massive or massless) or a massive vector field. As an application, we study the evolution of the interaction rate per particle under the relaxation time approximation, and assess when a given self-interaction is relevant in comparison with the Hubble expansion rate. Our framework aims to be a useful starting point to evaluate DM self-interaction effects in the linear power spectrum, necessary to then study its evolution all the way to non-linear stages of structure formation, where certain DM interactions were proven to be relevant., Comment: Published in Journal of Cosmology and Astroparticle Physics, 57 pages, 3 figures and 4 appendices

In this paper we consider a parity violating gravity model without higher derivatives, thus ghost free. This model is constructed from the tetrad and its derivatives and coupled to a dynamical scalar field, like axion. It can be reduced from the Nieh-Yan term within the framework of teleparallel gravity. We apply this model to cosmology and investigate its consequences on cosmological perturbation theory. We find that the coupled dynamical scalar field lost its independent dynamics at the linear order and the parity violating term itself behaves like a viscosity. For gravitational waves, this model produces velocity difference between left- and right-handed polarizations, but generates no amplitude discrepancy., The version matches the one to appear in JCAP

The peculiar velocities of biased tracers of the cosmic density field contain important information about the growth of large scale structure and generate anisotropy in the observed clustering of galaxies. Using N-body data, we show that velocity expansions for halo redshift-space power spectra are converged at the percent-level at perturbative scales for most line-of-sight angles $\mu$ when the first three pairwise velocity moments are included, and that the third moment is well-approximated by a counterterm-like contribution. We compute these pairwise-velocity statistics in Fourier space using both Eulerian and Lagrangian one-loop perturbation theory using a cubic bias scheme and a complete set of counterterms and stochastic contributions. We compare the models and show that our models fit both real-space velocity statistics and redshift-space power spectra for both halos and a mock sample of galaxies at sub-percent level on perturbative scales using consistent sets of parameters, making them appealing choices for the upcoming era of spectroscopic, peculiar-velocity and kSZ surveys., Comment: 63 pages, 11 figures, updated to match version accepted by JCAP

The Fourier-space galaxy bispectrum is complex, with the imaginary part arising from leading-order relativistic corrections, due to Doppler, gravitational redshift and related line-of-sight effects in redshift space. The detection of the imaginary part of the bispectrum is potentially a smoking gun signal of relativistic contributions. We investigate whether next-generation spectroscopic surveys could make such a detection. For a Stage IV spectroscopic $H\alpha$ survey similar to Euclid, we find that the cumulative signal to noise of this relativistic signature is $\mathcal{O}(10)$. Long-mode relativistic effects couple to short-mode Newtonian effects in the galaxy bispectrum, but not in the galaxy power spectrum. This is the basis for detectability of relativistic effects in the bispectrum of a single galaxy survey, whereas the power spectrum requires multiple galaxy surveys to detect the corresponding signal., Comment: 13 pages, 10 figures, Typo in equation (3.8) corrected - results unchanged

A variety of gauges are used in cosmological perturbation theory. These are often chosen in order to attribute physical properties to a particular choice of coordinates, or otherwise to simplify the form of the resultant equations. Calculations are then performed with the understanding that they could have been done in any gauge, and that transformations between different gauges can be made at will. We show that this logic can be extended to the domain of large density contrasts, where different types of perturbative expansion are required, but that the way in which gauges can be chosen in the presence of such structures is severely constrained. In particular, most gauges that are commonly considered in the cosmology literature are found to be unviable in the presence of non-linear structures. This includes spatially flat gauge, synchronous gauge, comoving orthogonal gauge, total matter gauge, N-body gauge, and the uniform density gauge. In contrast, we find that the longitudinal gauge and the Newtonian motion gauge are both viable choices in both standard cosmological perturbation theory, and in the post-Newtonian perturbative expansions that are required in order to model non-linear structures., Comment: 15 pages, 2 figures

We use anisotropic fluid cosmology to describe the present, dark energy-dominated, universe. Similarly to what has been proposed for galactic dynamics, the anisotropic fluid gives an effective description of baryonic matter, dark energy and their possible interaction, without assuming the presence of dark matter. The resulting anisotropic fluid spacetime naturally generates inhomogeneities at small scales, triggered by an anisotropic stress, and could therefore be responsible for structure formation at these scales. Solving the cosmological equations, we show that the dynamics of the scale factor $a$ is described by usual FLRW cosmology and decouples completely from that describing inhomogeneities. We assume that the cosmological anisotropic fluid inherits the equation of state from that used to describe galaxy rotation curves. We show that, in the large scale regime, the fluid can be described as a generalized Chaplygin gas and fits well the distance modulus experimental data of type Ia supernovae, thus correctly modelling the observed accelerated expansion of the universe. Conversely, in the small scale regime, we use cosmological perturbation theory to derive the power spectrum $P(k)$ for mass density distribution. At short wavelengths, we find a $1/k^4$ behaviour, in good accordance with the observed correlation function for matter distribution at small scales., 20 pages, 1 figure

We study the phenomenology of the beyond Horndeski class of scalar-tensor theories of gravity, which on cosmological scales can be characterised in terms of one extra function of time, $\alpha_{\rm H}$, as well as the usual four Horndeski set of free functions. We show that $\alpha_{\rm H}$ can be directly related to the the damping of the matter power spectrum on both large and small scales. We also find that the temperature power spectrum of the cosmic microwave background (CMB) is enhanced at low multipoles and the lensing potential is decreased, as a function of $\alpha_{\rm H}$. We find constraints on $\alpha_{\rm H}$ of order ${\cal O}(1)$ using measurements of the temperature and polarisation of the CMB, as well as the lensing potential derived from it, combined with large scale structure data. We find that redshift space distortion measurements can play a significant role in constraining these theories. Finally, we comment on the recent constraints from the observation of an electromagnetic counterpart to a gravitational wave signal; we find that these constraints reduce the number of free parameters of the model but do not significantly change the constraints on the remaining parameters., Comment: 33 pages; 10 figures; 4 tables; Version as accepted for publication in JCAP

Large scale density modes are difficult to measure because they are sensitive to systematic observational errors in galaxy surveys, but we can study them indirectly by observing their impact on small scale perturbations. Cosmological perturbation theory predicts that second-order density inhomogeneities are a convolution of a short- and a long-wavelength mode. This arises physically because small scale structures grow at different rates depending on the large scale environment in which they reside. This induces an off-diagonal term in the two-point statistics in Fourier space that we use as the basis for a quadratic estimator for the large scale field. We demonstrate that this quadratic estimator works well on an N-body simulation of size (2.5 h^{-1} Gpc)^3. In particular, the quadratic estimator successfully reconstructs the long-wavelength modes using only small-scale information. This opens up novel opportunities to study structure on the largest observable scales., 4 pages, 4 figures

We present two new covariant and general prescriptions for averaging scalar observables on spatial regions typical of the observed sources and intersecting the past light-cone of a given observer. One of these prescriptions is adapted to sources exactly located on a given space-like hypersurface, the other applies instead to situations where the physical location of the sources is characterized by the experimental "spread" of a given observational variable. The geometrical and physical differences between the two procedures are illustrated by computing the averaged energy flux received by distant sources located on (or between) constant redshift surfaces, and by working in the context of a perturbed $\Lambda$CDM geometry. We find significant numerical differences (of about ten percent or more, in a large range of redshift) even limiting our model to scalar metric perturbations, and stopping our computations to the leading non-trivial perturbative order., Comment: 29 pages, 7 figures. Several comments added, comparison with previous results improved, references added. Version accepted for publication on JCAP

We discuss the possibility of producing a significant fraction of dark matter in the form of primordial black holes in the context of the pre-big bang inflationary scenario. We take into account, to this purpose, the enhancement of curvature perturbations possibly induced by a variation of the sound-speed parameter $c_s$ during the string phase of high-curvature inflation. After imposing all relevant observational constraints, we find that the considered class of models is compatible with the production of a large amount of primordial black holes in the mass range relevant to dark matter, provided the sound-speed parameter is confined in a rather narrow range of values, $0.003 < c_s < 0.01$., 26 pages, two figures. Many new references and a few comments added. Version accepted for publication in JCAP

We study cosmological perturbation theory in the cosmology associated with conformal gravity, establish the validity of the decomposition theorem for it, and then use the theorem to provide an exact solution to the theory in the recombination era. Central to our approach is the use of a fully gauge invariant formulation of the cosmological fluctuations equations. In the recombination era not only is perturbation theory applicable, because of its specific structure in the conformal case the fluctuation equations are found to greatly simplify. Using a master equation for scalar, vector and tensor fluctuation modes we show that the radial equations for the three-dimensional vector and tensor modes are respectively the same as those of scalar modes in five and seven spatial dimensions. This enables us to construct normalization conditions for the three-dimensional modes., Comment: Expanded version. 41 pages. Final version, to appear in Phys. Rev. D

Next-generation galaxy and 21cm intensity mapping surveys will rely on a combination of the power spectrum and bispectrum for high-precision measurements of primordial non-Gaussianity. In turn, these measurements will allow us to distinguish between various models of inflation. However, precision observations require theoretical precision at least at the same level. We extend the theoretical understanding of the galaxy bispectrum by incorporating a consistent general relativistic model of galaxy bias at second order, in the presence of local primordial non-Gaussianity. The influence of primordial non-Gaussianity on the bispectrum extends beyond the galaxy bias and the dark matter density, due to redshift-space effects. The standard redshift-space distortions at first and second order produce a well-known primordial non-Gaussian imprint on the bispectrum. Relativistic corrections to redshift-space distortions generate new contributions to this primordial non-Gaussian signal, arising from: (1)~a coupling of first-order scale-dependent bias with first-order relativistic observational effects, and (2)~linearly evolved non-Gaussianity in the second-order velocity and metric potentials which appear in relativistic observational effects. Our analysis allows for a consistent separation of the relativistic `contamination' from the primordial signal, in order to avoid biasing the measurements by using an incorrect theoretical model. We show that the bias from using a Newtonian analysis of the squeezed bispectrum could be $\Delta \fnl\sim 5$ for a Stage IV H$\alpha$ survey., Comment: Version accepted by JCAP (JCAP_030P_1220) + 18 pages + 4 figures + appendices + references

Within cosmological perturbation theory, the cosmic microwave background anisotropies are usually computed from a Boltzmann hierarchy coupled to the perturbed Einstein equations. In this setup, one set of multipoles describes the temperature anisotropies, while two other sets, of electric and magnetic types, describe the polarization anisotropies. In order to reduce the number of multipoles types needed for polarization, and thus to speed up the numerical resolution, an optimal hierarchy has been proposed in the literature for Einstein-Boltzmann codes. However, it has been recently shown that the separability between directional and orbital eigenfunctions employed in the optimal hierarchy is not correct in the presence of spatial curvature. We investigate how the assumption of separability affects the optimal hierarchy, and show that it introduces relative errors of order $\Omega_K$ with respect to the full hierarchy. Despite of that, we show that the optimal hierarchy still gives extremely good results for temperature and polarization angular spectra, with relative errors that are much smaller than cosmic variance even for curvatures as large as $|\Omega_K|=0.1$. Still, we find that the polarization angular spectra from tensor perturbations are significantly altered when using the optimal hierarchy, leading to errors that are typically of order $50 |\Omega_K| \%$ on that component., Comment: 12 pages, 2 figures

Inspired by the fully non-linear Geodesic Light-Cone (GLC) gauge, we consider its analogous set of coordinates which describes the unperturbed Universe. Given this starting point, we then build a cosmological perturbation theory on top of it, study the gauge transformation properties related to this new set of perturbations and show the connection with standard cosmological perturbation theory. In particular, we obtain which gauge in standard perturbation theory corresponds to the GLC gauge, and put in evidence how this is a useful alternative to the standard Synchronous Gauge. Moreover, we exploit several viable definitions for gauge invariant combinations. Among others, we build the gauge invariant variables such that their values equal the ones of linearized GLC gauge perturbations. This choice is motivated by two crucial properties of the GLC gauge: i) it admits simple expressions for light-like observables, e.g. redshift and angular distance, at fully non-linear level and ii) the GLC proper time coincides with the one of a free-falling observer. Thanks to the first property, exact expressions can then be easily expanded at linear order to obtain linear gauge invariant expression for the chosen observable. Moreover, the second feature naturally provides gauge invariant expressions for physical observables in terms of the time as measured by such free-falling observer. Finally, we explicitly show all these aspects for the case of the linearized angular distance-redshift relation., Comment: 26 pages, no figures. Inconsequential modification of an equation. Comments and references added. Version accepted for publication in JCAP

We study the impact of the viscous effects of the primordial plasma on the evolution of the primordial gravitational waves (pGW) spectrum from Inflation until today, considering a self-consistent interaction that incorporates the back-reaction of the GW into the plasma. We use a relativistic causal hydrodynamic framework with a positive entropy production based on a Second-Order Theory (SOT) in which the viscous properties of the fluid are effectively described by a new set of independent variables. We study how the spin-2 modes typical of SOTs capture the simplest GW-fluid viscous interaction to first order. We consider that all non-ideal properties of the primordial plasma are due to an extra effectively massless self-interacting scalar field whose state becomes a many-particles one after Reheating and for which an effective fluid description is suitable. We numerically solve the evolution equations and explicitly compute the current GW spectrum obtaining two contributions. On the one hand we have the viscous evolution of the pGW: For the collision-dominated regime the GW source becomes negligible while in the collisionless limit there exists an absorption of the pGW energy due to the damping effect produced by the free-streaming spin-2 modes of the fluid and driven by the expansion of the Universe. The latter effect is characterized by a relative amplitude decrease of about 1 to 10 \% with respect to the GW free evolution spectrum. On the other hand we get the GW production due to the decay of the initial spin-2 fluctuations of the fluid that is negligible compared with the above-mentioned contribution. This SOT framework captures the same qualitative effects on the evolution of GW coupled to matter reported in previous works in which a kinetic theory approach has been used., Comment: 29 pages, 3 figures, comparison with the kinetic theory approach included; matches the published version

Gravitational waves (GWs) induced by scalar curvature fluctuations are an important source of the cosmological GW background and a crucial counterpart of the primordial black hole scenario. However, doubts have been cast on the theoretically predicted induced GW spectrum due to its seeming gauge dependence. In this paper, we shed light on the gauge dependence issue of the induced GW spectrum in general cosmological backgrounds. First, inspired by the Hamiltonian formalism we provide very simple formulas for the tensor modes at second order in cosmological perturbation theory. We also emphasize the difference between observable and gauge invariant variables. Second, we argue that the Newton (or shear-free) gauge is suitable for both the calculation of induced GWs and the physical interpretation. We then show that, most notably, the induced GW spectrum is invariant under a set of reasonable gauge transformations, i.e. physically well behaved on small scales, once the source term has become inactive. This includes the commonly used flat, constant Hubble and synchronous gauges but excludes the comoving slicing gauge. We also show that a particular solution of the GW equation in a dust dominated universe while the source term is active can be gauged away by a small change of gauge., Comment: Typos corrected, matches published version