Scalar Cosmological Perturbations Research Articles

Selecting energy–momentum trace dependent gravity theories with LSS

We study scalar cosmological perturbations in f(R,T) modified gravity theories, where T represents the trace of the energy–momentum tensor. We provide detailed equations for the matter energy density contrast. We solve them numerically to facilitate a comparison with available large-scale structure (LSS) formation observational data on fσ8, while also addressing the S8 tension. We identify f(R,T) models that either lead to growth enhancement or suppression. Since recent results in the literature indicate a preference for the latter feature, this type of analysis is quite useful for selecting viable modifications of gravity. The studied class of such f(R,T) models are either ruled out or severely restricted. After selecting the surviving f(R,T) models we show how they deal with the S8 tension.

Cosmological higher-curvature gravities

We examine higher-curvature gravities whose Friedmann–Lemaître–Robertson–Walker configurations are specified by equations of motion which are of second order in derivatives, just like in Einstein gravity. We name these theories Cosmological Gravities and initiate a systematic exploration in dimensions D⩾3 . First, we derive an instance of Cosmological Gravity to all curvature orders and dimensions D⩾3 . Second, we study Cosmological Gravities admitting non-hairy generalizations of the Schwarzschild solution characterized by a single function whose equation of motion is, at most, of second order in derivatives. We present explicit instances of such theories for all curvature orders and dimensions D⩾4 . Finally, we investigate the equations of motion for cosmological perturbations in the context of generic Cosmological Gravities. Remarkably, we find that the linearized equations of motion for scalar cosmological perturbations in any Cosmological Gravity in D⩾3 contain no more than two time derivatives. We explicitly corroborate this aspect by presenting the equations for the scalar perturbations in some four-dimensional Cosmological Gravities up to fifth order in the curvature.

Primordial gravitational waves assisted by cosmological scalar perturbations

Primordial gravitational waves are a crucial prediction of inflation theory, and their detection through their imprints on the cosmic microwave background is actively being pursued. However, these attempts have not yet been successful. In this paper, we propose a novel approach to detect primordial gravitational waves by searching for a signal of second-order tensor perturbations. These perturbations were produced due to nonlinear couplings between the linear tensor and scalar perturbations in the early universe. We anticipate a blue-tilted tensor spectral index, and suggest that the tensor-to-scalar ratio can potentially be measured with high precision using a detector network composed of the ground-based Einstein Telescope and the space-borne LISA project on a decade timescale.

Primordial non-Gaussianity f NL and anisotropies in scalar-induced gravitational waves

Primordial non-Gaussianity encodes vital information of the physics of the early universe, particularly during the inflationary epoch. To explore the local-type primordial non-Gaussianity f NL, we study the anisotropies in gravitational wave background induced by the linear cosmological scalar perturbations during radiation domination in the early universe. We provide the first complete analysis to the angular power spectrum of such scalar-induced gravitational waves. The spectrum is expressed in terms of the initial inhomogeneities, the Sachs-Wolfe effect, and their crossing. It is anticipated to have frequency dependence and multipole dependence, i.e., Cℓ (ν) ∝ [ℓ(ℓ+1)]-1 with ν being a frequency and ℓ referring to the ℓ-th spherical harmonic multipole. In particular, the initial inhomogeneites in this background depend on gravitational-wave frequency. These properties are potentially useful for the component separation, foreground removal, and breaking degeneracies in model parameters, making the non-Gaussian parameter f NL measurable. Further, theoretical expectations may be tested by space-borne gravitational-wave detectors in future.

Extended minimal theories of massive gravity

In this work, we introduce a class of extended Minimal Theories of Massive Gravity (eMTMG), without requiring a priori that the theory should admit the same homogeneous and isotropic cosmological solutions as the de Rham-Gabadadze-Tolley massive gravity. The theory is constructed as to have only two degrees of freedom in the gravity sector. In order to perform this step we first introduce a precursor theory endowed with a general graviton mass term, to which, at the level of the Hamiltonian, we add two extra constraints as to remove the unwanted degrees of freedom, which otherwise would typically lead to ghosts and/or instabilities. On analyzing the number of independent constraints and the properties of tensor mode perturbations, we see that the gravitational waves are the only propagating gravitational degrees of freedom which do acquire a non-trivial mass, as expected. In order to understand how the effective gravitational force works for this theory we then investigate cosmological scalar perturbations in the presence of a pressureless fluid. We then restrict the whole class of models by imposing the following conditions at all times: 1) it is possible to define an effective gravitational constant, $G_{{\rm eff}}$; 2) the value $G_{\text{eff}}/G_{N}$ is always finite but not always equal to unity (as to allow some non-trivial modifications of gravity, besides the massive tensorial modes); and 3) the square of mass of the graviton is always positive. These constraints automatically make also the ISW-effect contributions finite at all times. Finally we focus on a simple subclass of such theories, and show they already can give a rich and interesting phenomenology.

Second-order energy-momentum tensor of a scalar field

We investigate the second-order effective energy-momentum tensor (2EMT) constructed by the quadratic terms of the linear scalar cosmological perturbations while the universe is dominated by a scalar field. We show that 2EMT is gauge dependent. We then study 2EMT in three (longitudinal, spatially flat, and comoving) gauge conditions in the slow-roll stage of inflation. We find that 2EMT exhibits an effective fluid of $w=\ensuremath{-}1/3$ on superhorizon scales in all of those gauge conditions.

Effective dynamics of scalar cosmological perturbations from quantum gravity

We derive an effective dynamics for scalar cosmological perturbations from quantum gravity, in the framework of group field theory condensate cosmology. The emergent spacetime picture is obtained from the mean-field hydrodynamic regime of the fundamental theory, and physical observables are defined using a relational strategy applied at the same level of approximation, in terms of suitable collective states of the GFT field. The dynamical equations we obtain for volume and matter perturbations lead to the same solutions as those of classical GR in the long-wavelength, super-horizon limit, but differ in other regimes. These differences could be of phenomenological interest and make contact between fundamental quantum gravity models and cosmological observations, indicating new physics or limitations of the fundamental models or of the approximations leading to the effective cosmological dynamics.

Spin connection and cosmological perturbations in scalar-torsion gravity

In this paper, we generalize our previous results on spin connection for the linear scalar cosmological perturbation in [Formula: see text] theory to a wider class of theories which includes a scalar field [Formula: see text] non-minimally coupled to torsion, and allows [Formula: see text]-dependence of the function [Formula: see text]. The case of [Formula: see text], with a scalar field non-minimally coupled to torsion, needs a special treatment. In both considered cases we derive self-consistent equations of motion for cosmological perturbation using a solution for non-trivial spin connection.

Effect of the Cubic Torus Topology on Cosmological Perturbations

We study the effect of the cubic torus topology of the Universe on scalar cosmological perturbations which define the gravitational potential. We obtain three alternative forms of the solution for both the gravitational potential produced by point-like masses, and the corresponding force. The first solution includes the expansion of delta-functions into Fourier series, exploiting periodic boundary conditions. The second one is composed of summed solutions of the Helmholtz equation for the original mass and its images. Each of these summed solutions is the Yukawa potential. In the third formula, we express the Yukawa potentials via Ewald sums. We show that for the present Universe, both the bare summation of Yukawa potentials and the Yukawa-Ewald sums require smaller numbers of terms to yield the numerical values of the potential and the force up to desired accuracy. Nevertheless, the Yukawa formula is yet preferable owing to its much simpler structure.

Intrinsic Entropy of Squeezed Quantum Fields and Nonequilibrium Quantum Dynamics of Cosmological Perturbations.

Density contrasts in the universe are governed by scalar cosmological perturbations which, when expressed in terms of gauge-invariant variables, contain a classical component from scalar metric perturbations and a quantum component from inflaton field fluctuations. It has long been known that the effect of cosmological expansion on a quantum field amounts to squeezing. Thus, the entropy of cosmological perturbations can be studied by treating them in the framework of squeezed quantum systems. Entropy of a free quantum field is a seemingly simple yet subtle issue. In this paper, different from previous treatments, we tackle this issue with a fully developed nonequilibrium quantum field theory formalism for such systems. We compute the covariance matrix elements of the parametric quantum field and solve for the evolution of the density matrix elements and the Wigner functions, and, from them, derive the von Neumann entropy. We then show explicitly why the entropy for the squeezed yet closed system is zero, but is proportional to the particle number produced upon coarse-graining out the correlation between the particle pairs. We also construct the bridge between our quantum field-theoretic results and those using the probability distribution of classical stochastic fields by earlier authors, preserving some important quantum properties, such as entanglement and coherence, of the quantum field.

Model independent prediction of the spectral index of primordial quantum fluctuations

One of the most important achievements of inflationary cosmology is to predict a departure from scale invariance of the power spectrum for cosmological scalar perturbations. This tilt is understood as a consequence of a quasi de Sitter classical equation of state describing the inflationary dark energy dominated era. Here, following previous work, we find a departure of scale invariance for the quantum Fisher information associated to de Sitter vacuum for scalar quantum spectator modes. This gives rise to a purely quantum cosmological tilt with a well defined dependence on energy scale. This quantum tilt is imprinted, in a scale dependent energy uncertainty for the spectator modes. The effective quasi de Sitter description of this model independent energy uncertainty uniquely sets the effective quasi de Sitter parameters (i.e., the small deviation from the cosmological constant equation of state) at all energy scales. In particular, in the slow-roll regime characterized by an almost constant ϵ, the quantum Fisher — model independent — prediction for the spectral index is n s = 0.9672. Moreover, the energy scale dependence of the quantum cosmological tilt implies the existence of a cosmological phase transition at energies higher than the CMB scale and of the order of 1 Mpc-1 where the tilt goes from red into blue. This strongly suggest the existence of a pre-inflationary phase where the effective scalaron contributes to the spectral index as normal relativistic matter and where the corresponding growth of the power spectrum can result in dark matter in the form of small mass primordial black holes. The source and features of the quantum cosmological tilt leading to these predictions are determined by the entanglement features of the de Sitter α- vacuum states.

Perturbations of quasi-Newtonian universes in scalar–tensor gravity

In this contribution, we consider the well-known equivalence between [Formula: see text] gravity and Brans–Dicke-type scalar–tensor theories to study the evolution of scalar cosmological perturbations for a class of shear-free cosmological dust models with irrotational fluid flows. We use the [Formula: see text] covariant formalism to present the covariant linearized evolution and constraint equations. We then derive the integrability conditions describing a consistent evolution of the linearized field equations of quasi-Newtonian universes in the modified (scalar–tensor) theory of gravity. Finally, we derive the evolution equations for the density and velocity perturbations of the quasi-Newtonian universe. We apply the harmonic decomposition and explore the behavior of the matter density contrast by considering [Formula: see text] toy models. The growth of the matter density contrast for both short- and long-wavelength modes has been examined by applying certain assumptions of the initial conditions. We then apply the so-called quasi-static approximation to obtain exact solutions on small scales, but the results show that this approximation is not applicable here. Moreover, any small deviation from general relativity and any small change in the initial conditions of the perturbations causes huge orders-of-magnitude deviations from limiting general relativistic results, potentially putting constraints on the modified theory in the quasi-Newtonian cosmologies treatment. Our current work differs from other works in the literature, in that it is the first such work to show quasi-Newtonian cosmologies are unstable to linearized perturbations in modified gravity.

Gravitational wave cosmology: High frequency approximation

In this paper, we systematically study gravitational waves (GWs) produced by remote compact astrophysical sources. To describe such GWs properly, we introduce three scales, $\lambda, \; L_c$ and $L$, denoting, respectively, the typical wavelength of GWs, the scale of the cosmological perturbations, and the size of the observable universe. For GWs to be detected by the current and foreseeable detectors, the condition $\lambda \ll L_c \ll L$ holds, and such GWs can be well approximated as high-frequency GWs. In order for the backreaction of the GWs to the background to be negligible, we must assume that $\left|h_{\mu\nu}\right| \ll 1$, in addition to the condition $\epsilon \ll 1$, which are also the conditions for the linearized Einstein field equations for $h_{\mu\nu}$ to be valid, where $g_{\mu\nu} = \gamma_{\mu\nu} + \epsilon h_{\mu\nu}$, and $\gamma_{\mu\nu}$ denotes the background. To simplify the field equations, we show that the spatial, traceless, and Lorentz gauge conditions can be imposed simultaneously, even when the background is not vacuum, as long as the high-frequency GW approximation is valid. However, to develop the formulas that can be applicable to as many cases as possible, we first write down explicitly the linearized Einstein field equations by imposing only the spatial gauge. Applying the general formulas together with the geometrical optics approximation to such GWs, we find that they still move along null geodesics and its polarization bi-vector is parallel-transported, even when both the cosmological scalar and tensor perturbations are present. In addition, we also calculate the gravitational integrated Sachs-Wolfe effects, whereby the dependences of the amplitude, phase and luminosity distance of the GWs on these two kinds of perturbations are read out explicitly.

Sub-horizon modes and growth index in a linear scalar cosmological perturbations

We test a four dimensional cosmological model embedded in a five dimensional bulk space by means of the dynamical Nash-Greene theorem. In a fluid approach, we apply a joint likelihood analysis to the data with the Markov Chain Monte Carlo (MCMC) method for cosmological parameter estimation. We use recent datasets as the “Gold 2018” growth-rate data, the Planck2018/varLambda CDM data on the cosmic microwave background (CMB) anisotropies, the Baryon acoustic oscillations (BAO) measurements, the Pantheon Supernovae type Ia and the data on the Hubble parameter H(z) with redshift ranging from 0.01< z < 2.3. Performing the Information Criterion (IC) analysis, we find that the present model is in very good agreement with observations with a close statistical equivalence with wCDM cosmologies at 1-sigma level with a slightly larger growth profiles. By modifications of CLASS(EFCLASS) code, we make a comparison between the models on their unlensed CMB TT temperature spectra. Moreover, the proposed model presents a low power spectrum by the reduction of the ISW effect at lower multipoles. We also find that the overall percentage relative difference of the growth index varDelta gamma (%) is up to 1.4% as compared to wCDM pattern in sub-horizon scales.

Energy of cosmological spacetimes and perturbations: a quasilocal approach * *Sections 2 and 3 of this paper are an expanded version of the essay ‘quasilocal conservation laws in cosmology: a first look’ [], awarded honorable mention in the gravity research foundation 2020 awards for essays on gravitation.

Quasilocal definitions of stress–energy–momentum—that is, in the form of boundary densities (rather than local volume densities)—have proven generally very useful in formulating and applying conservation laws in general relativity. In this paper, we present a detailed application of such definitions to cosmology, specifically using the Brown–York quasilocal stress–energy–momentum tensor for matter and gravity combined. We compute this tensor, focusing on the energy and its associated conservation law, for FLRW spacetimes with no pertubrations and with scalar cosmological perturbations. For unperturbed FLRW spacetimes, we emphasize the importance of the vacuum energy (for both flat and curved space), which is almost universally underappreciated (and usually ‘subtracted’), and discuss the quasilocal interpretation of the cosmological constant. For the perturbed FLRW spacetime, we show how our results recover or relate to the more typical effective local treatment of energy in cosmology, with a view toward better studying the issues of the cosmological constant and of cosmological back-reactions.

Scalar cosmological perturbations in M-theory with higher-derivative corrections

Abstract We investigate the inflationary expansion of the universe induced by higher-curvature corrections in M-theory. The inflationary evolution of the geometry is discussed in K. Hiraga and Y. Hyakutake, Prog. Theor. Exp. Phys. 2018, 113B03 (2018), which we follow to analyze metric perturbations around the background. We especially focus on scalar perturbations and analyze linearized equations of motion for the scalar perturbations. By solving these equations explicitly, we evaluate the power spectrum of the curvature perturbation. The scalar spectrum index is estimated under some assumptions, and we show that it becomes close to 1.

On (non-)dynamical dark energy

The current Universe is composed by a mixture of relativistic species, baryonic matter, dark matter and dark energy which evolve in a non-trivial way at perturbative level. An advanced description of the cosmological dynamics should include non-standard features beyond the simplistic approach idealized by the standard cosmology in which cosmic components do not interact, are adiabatic and dissipationless. We promote a full perturbative analysis of linear scalar perturbations of a non-interacting cosmological model containing baryons, dark matter (both pressureless) and a scalar field allowing for the presence of relative entropic perturbations between the three fluids. Assuming an effective scalar-field sound speed equal to one and neglecting anisotropic stresses we establish a new set of equations for the scalar cosmological perturbations. As a consequence of this new approach, we show that tiny departures from a constant scalar field equation of state $w_S=-1$ damage structure formation in a non-acceptable manner. Hence, by strongly constraining $w_S$ our results provide compelling evidence in favor of the standard cosmological model and rule out a large class of dynamical dark energy models

Scalar perturbations in f(T) gravity using the 1 + 3 covariant approach

The cosmological scalar perturbations of standard matter are investigated in the context of extended teleparallel f(T) gravity theories using the 1+3 covariant formalism. After a review of the background gravitational field equations of f(T) gravity and the introduction of the covariant perturbation variables, the usual scalar and harmonic decomposition have been performed, and the analysis of the growth of the density contrasts in the quasi-static approximation for two non-interacting fluids scenarios, namely torsion-dust and torsion-radiation mixtures is presented for the generic f(T) gravity theory. Special applications to two classes of f(T) gravity toy models, namely f(T) = mu T_0 Big (frac{T}{T_0}Big )^n and f(T) = T+ mu T_0 Big (-frac{T}{T_0}Big )^n, have then been made within the observationally viable regions of their respective parameter spaces, and the growth of the matter density contrast for both torsion-dust and torsion-radiation epochs of the Universe has been examined. The exact solutions of the dust perturbations, with growing amplitudes in cosmic time, are obtained for some limiting cases of n. Similarly, the long- and short-wavelength modes in the torsion-radiation case are treated, with the amplitudes either oscillating or monotonically growing with time. Overall, it is noted that f(T) models contain a richer set of observationally viable structure growth scenarios that can be tested against up-and-coming observational data and can accommodate currently known features of the large-scale structure power spectrum in the general relativistic and varLambda CDM limits.

Inflationary perturbation spectra at next-to-leading slow-roll order in effective field theory of inflation

The effective field theory (EFT) of inflation provides an essential picture to explore the effects of the unknown high energy physics in the single scalar field inflation models. For a generic EFT of inflation, possible high energy corrections to simple slow-roll inflation can modify both the propagating speed and dispersion relations of the cosmological scalar and tensor perturbations. With the arrival of the era of precision cosmology, it is expected that these high energy corrections become more important and have to be taken into account in the analysis with future precise observational data. In this paper we study the observational predictions of the EFT of inflation by using the third-order uniform asymptotic approximation method. We calculate explicitly the primordial power spectra, spectral indices, running of the spectral indices for both scalar and tensor perturbations, and the ratio between tensor and scalar spectra. These expressions are all written in terms of the Hubble flow parameters and the flow of four new slow-roll parameters and expanded up to the next-to-leading order in the slow-roll expansions so they represent the most accurate results obtained so far in the literature. The flow of the four new slow-roll parameters, which arise from the four new operators introduced in the action of the EFT of inflation, can affect the primordial perturbation spectra at the leading-order and the corresponding spectral indices at the next-to-leading order.

CMB circular and B -mode polarization from new interactions

Standard models describing the radiation transfer of the cosmic microwave background (CMB) through Compton scattering predict that cosmological scalar perturbations at linear order are not able to source V and B polarization modes. In this work, we investigate the possibility that such CMB polarization modes are generated even in the presence of linear scalar perturbations only. We provide a general parametrization of the photon-fermion forward-scattering amplitude and compute mixing terms between different CMB polarization modes. We discuss different general extensions of Standard Model interactions which violate discrete symmetries, while preserving the combination of charge conjugation, parity and time reversal. We show that it is possible to source CMB circular polarization by violating parity and charge conjugation symmetries. Instead, B-mode generation is associated to the violation of symmetry for time-reversal. Our results provide a useful tool to constrain new physics using CMB data.