Recent analyses of the Planck data and quasars at high redshifts have suggested possible deviations from the flat $Λ$ cold dark matter model ($Λ$CDM), where $Λ$ is the cosmological constant. Here we use machine learning methods to investigate any possible deviations from $Λ$CDM at both low and high redshifts by using the latest cosmological data. Specifically, we apply the Genetic Algorithms to explore the nature of dark energy (DE) in a model independent fashion by reconstructing its equation of state $w(z)$, the growth index of matter density perturbations $γ(z)$, the linear DE anisotropic stress $η_\textrm{DE}(z)$ and the adiabatic sound speed $c_\textrm{s,DE}^2(z)$ of DE perturbations. We find a $\sim2σ$ deviation of $w(z)$ from -1 at high redshifts, the adiabatic sound speed is negative at the $\sim2.5σ$ level at $z=0.1$ and a $\sim2σ$ deviation of the anisotropic stress from unity at low redshifts and $\sim4 σ$ at high redshifts. These results hint towards either the presence of an non-adiabatic component in the DE sound speed or the presence of DE anisotropic stress, thus hinting at possible deviations from the $Λ$CDM model.
Gravitational waves (GWs) are inevitably induced at second-order in cosmological perturbations through non-linear couplings with first order scalar perturbations, whose existence is well established by recent cosmological observations. So far, the evolution and the spectrum of the secondary induced GWs have been derived by taking into account the sources of GWs only from the product of first order scalar perturbations. Here we newly investigate the effects of purely second-order anisotropic stresses of photons and neutrinos on the evolution of GWs, which have been omitted in the literature. We…
The effective anisotropic stresses induced by the scalar modes of the geometry depend on the coordinate system so that the comparison of the competing results is ultimately determined by the evolution of the pivotal variables in each particular gauge. After arguing that the only reasonable physical coordinate systems for this problem are the ones where the gauge freedom is completely fixed (like the longitudinal and the uniform curvature gauges), we propose a novel gauge-invariant strategy for the comparison of gauge-dependent results. Instead of employing the pivotal variables of a given coor…
The existence of anisotropic stress of a purely geometrical origin seems to be a characteristic of higher order gravity models, and has been suggested as a probe to test these models observationally, for example in weak lensing experiments. In this paper, we seek to find a class of higher order gravity models of f(R,G) type that would give us a zero anisotropic stress and study the consequences for the viability of the actual model. For the special case of a de Sitter background, we identify a subclass of models with the desired property. We also find a direct link between anisotropic stress a…
One of the main goal of large-scale structure surveys is to test the consistency of General Relativity at cosmological scales. In the $Λ$CDM model of cosmology, the relations between the fields describing the geometry and the content of our Universe are uniquely determined. In particular, the two gravitational potentials -- that describe the spatial and temporal fluctuations in the geometry -- are equal. Whereas large classes of dark energy models preserve this equality, theories of modified gravity generally create a difference between the potentials, known as anisotropic stress. Even though …
We make precise the heretofore ambiguous statement that anisotropic stress is a sign of a modification of gravity. We show that in cosmological solutions of very general classes of models extending gravity --- all scalar-tensor theories (Horndeski), Einstein-Aether models and bimetric massive gravity --- a direct correspondence exists between perfect fluids apparently carrying anisotropic stress and a modification in the propagation of gravitational waves. Since the anisotropic stress can be measured in a model-independent manner, a comparison of the behavior of gravitational waves from cosmol…
It is always interesting to investigate how well can a future experiment perform with respect to others (present or future ones). Cosmology is really an exciting field where a lot of puzzles are still unknown. In this article we consider a generalized dark energy (DE) scenario where anisotropic stress is present. We constrain this generalized cosmic scenario with an aim to investigate how gravitational waves standard sirens (GWSS) may constrain the anisotropic stress, which according to the standard cosmological probes, remains unconstrained. In order to do this, we generate the luminosity dis…
The large-scale structure of the Universe is a rich source of information to test the consistency of General Relativity on cosmological scales. We briefly describe how the observed distributions of galaxies is affected by redshift-space distortions, but also by gravitational lensing and other relativistic effects. Then, we show how one of this relativistic effects, the gravitational redshift, can be used to build a model independent test that directly measures the anisotropic stress, i.e. the difference between the two gravitational potentials that describe spacetime fluctuations of the geomet…
The large-scale curvature perturbations induced by spectator anisotropic stresses are analyzed across the matter-radiation transition. It is assumed that the anisotropic stress is associated with a plasma component whose energy density is subdominant both today and prior to photon decoupling. The enforcement of the momentum constraint and the interplay with the neutrino anisotropic stress determine the regular initial conditions of the Einstein-Boltzmann hierarchy. The Cosmic Microwave Background observables have shapes and phases which differ both from the ones of the conventional adiabatic m…
We expand previous work on an inverse approach to Einstein Field Equations where we include fluids with energy flux and consider the vanishing of the anisotropic stress tensor. We consider the approach using warped product spacetimes of class $B_1$. Although restricted, these spacetimes include many exact solutions of interest to compact object studies and to cosmological models studies. The question explored here is as follows: given a spacetime metric, what fluid flow (timelike congruence), if any, could generate the spacetime via Einstein's equations. We calculate the flow from the conditio…
We study the effects of dark energy (DE) anisotropic stress on features of the matter power spectrum (PS). We employ the Parametrized Post-Friedmannian (PPF) formalism to emulate an effective DE, and model its anisotropic stress properties through a two-parameter equation that governs its overall amplitude ($g_0$) and transition scale ($c_g$). For the background cosmology, we consider different equations of state to model DE including a constant $w_0$ parameter, and models that provide thawing (CPL) and freezing (nCPL) behaviors. We first constrain these parameters by using the Pantheon, BAO, …
We study the evolution of curvature perturbations and the cosmic microwave background (CMB) power spectrum in the presence of an hypothesized extra anisotropic stress which might arise, for example, from the dark radiation term in brane-world cosmology. We evolve the scalar modes of such perturbations before and after neutrino decoupling and analyze their effects on the CMB spectrum. A novel result of this work is that the cancellation of the neutrino and extra anisotropic stress could lead to a spectrum of residual curvature perturbations which is similar to the observed CMB power spectrum. T…
We present the generalization of previously published results, about the perturbed redshift and the luminosity-redshift relation up to second order in perturbation theory, for the case of the Poisson gauge and in the presence of anisotropic stress. The results are therefore valid for general dark energy models and (most) modified gravity models. We use an innovative approach based on the recently proposed "geodesic light-cone" gauge. We then compare our finding with other results, which recently appeared in the literature, for the particular case of vanishing anisotropic stress. Arriving at a …
We study a novel interacting dark energy $-$ dark matter scenario where the anisotropic stress of the large scale inhomogeneities is considered. The dark energy has a constant equation of state and the interaction model produces stable perturbations. The resulting picture is constrained using different astronomical data aiming to measure the impact of the anisotropic stress on the cosmological parameters. Our analyses show that a non-zero interaction in the dark sector is allowed while a non-interaction scenario is recovered within 68\% CL. The anisotropic stress is also constrained to be smal…
In this work, we use recent data on the Hubble expansion rate $H(z)$, the quantity $fσ_8(z)$ from redshift space distortions and the statistic $E_g$ from clustering and lensing observables to constrain in a model-independent way the linear anisotropic stress parameter $η$. This estimate is free of assumptions about initial conditions, bias, the abundance of dark matter and the background expansion. We denote this observable estimator as $η_{\rm obs}$. If $η_{\rm obs}$ turns out to be different from unity, it would imply either a modification of gravity or a non-perfect fluid form of dark energ…
We study a dark energy model with non-zero anisotropic stress, either linked to the dark energy density or to the dark matter density. We compute approximate solutions that allow to characterise the behaviour of the dark energy model and to assess the stability of the perturbations. We also determine the current limits on such an anisotropic stress from the cosmic microwave background data by the Planck satellite, and derive the corresponding constraints on the modified growth parameters like the growth index, the effective Newton's constant and the gravitational slip.
We use the currently available cosmic observations to probe and constrain an imperfect dark energy fluid which is characterized by a constant equation of state $w$ and a constant speed of viscosity $c^2_{vis}$. The model parameter space was scanned by using Markov chain Monte Carlo method. The results show that the speed of viscosity $c^2_{vis}$ was not well constrained when currently available date sets, which include the cosmic microwave background radiation from {\it Planck}2013, type Ia supernovae and baryon acoustic oscillations, are used. But the cosmic data sets favor phantom dark energ…
The effective anisotropic stress or gravitational slip $η=-Φ/Ψ$ is a key variable in the characterisation of the physical origin of the dark energy, as it allows to test for a non-minimal coupling of the dark sector to gravity in the Jordan frame. It is however important to use a fully model-independent approach when measuring $η$ to avoid introducing a theoretical bias into the results. In this paper we forecast the precision with which future large surveys can determine $η$ in a way that only relies on directly observable quantities. In particular, we do not assume anything concerning the in…
Motivated by studies on gravitational lenses, we present an exact solution of the field equations of general relativity, which is static and spherically symmetric, has no mass but has a non-vanishing spacelike components of the stress-energy-momentum tensor. In spite of its strange nature, this solution provides with non-trivial descriptions of gravitational effects. We show that the main aspects found in the \emph{dark matter phenomena} can be satisfactorily described by this geometry. We comment on the relevance it could have to consider non-vanishing spacelike components of the stress-energ…
We investigate future constraints on early dark energy (EDE) achievable by the Planck and CMBPol experiments, including cosmic microwave background (CMB) lensing. For the dark energy, we include the possibility of clustering through a sound speed c_s^2 <1 (cold dark energy) and anisotropic stresses parameterized with a viscosity parameter c_vis^2. We discuss the degeneracies between cosmological parameters and EDE parameters. In particular we show that the presence of anisotropic stresses in EDE models can substantially undermine the determination of the EDE sound speed parameter c_s^2. The co…
On the basis of a previously established scalar-tensor extension of the $Λ$CDM model we develop an effective fluid approach for the matter growth function. This extended $Λ$CDM (henceforth $e_ΦΛ$CDM) cosmology takes into account deviations from the standard model both via a modified background expansion and by the inclusion of geometric anisotropic stresses as well as of perturbations of the geometric dark-energy equivalent. The background dynamics is governed by an explicit analytic expression for the Hubble rate in which modifications of the standard model are given in terms of a single cons…
