Gravitational Slip Parameter Research Articles

Gravitational slip parameter and gravitational waves in Einstein–Cartan theory

We study the evolution of scalar and tensor cosmological perturbations in the framework of the Einstein–Cartan theory of gravity. The value of the gravitational slip parameter which is defined as the ratio of the two scalar potentials in the Newtonian gauge, can be used to determine whether or not the gravity is modified. We calculate the value of slip parameter in the Einstein–Cartan cosmology and show that it falls within the observed range. We also discuss the evolution of the cosmic gravitational waves as another measure of the modification of gravity.

Probing gravitational slip with strongly lensed fast radio bursts

The rapid accumulation of observed Fast Radio Bursts (FRBs) originating from cosmological distances makes it likely that some will be strongly lensed by intervening matter along the line of sight. Detection of lensed FRB repeaters, which account for a noteworthy fraction of the total population, will allow not only an accurate measurement of the lensing time delay, but also follow-up high-resolution observations to pinpoint the location of the lensed images. Recent works proposed to use such strongly-lensed FRBs to derive constraints on the current expansion rate $ H_{0} $ as well as on cosmic curvature. Here we study the prospects for placing constraints on departures from general relativity via such systems. Using an ensemble of simulated events, we focus on the gravitational slip parameter $\gamma_{\rm PN}$ in screened modified gravity models and show that FRB time-delay measurements can yield constraints as tight as $ \left| \gamma_{\rm PN}-1\right| \lesssim 0.04\times(\Lambda/100\rm kpc)\times[N/10]^{-1/2} $ at $1\sigma$ with $10$ detections.

Stealth dark energy in scordatura DHOST theory

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 ΛCDM 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.

J-PAS: forecasts on dark energy and modified gravity theories

ABSTRACT The next generation of galaxy surveys will allow us to test one of the most fundamental assumptions of the standard cosmology, i.e. that gravity is governed by the general theory of relativity (GR). In this paper, we investigate the ability of the Javalambre Physics of the Accelerating Universe Astrophysical Survey (J-PAS) to constrain GR and its extensions. Based on the J-PAS information on clustering and gravitational lensing, we perform a Fisher matrix forecast on the effective Newton constant, μ, and the gravitational slip parameter, η, whose deviations from unity would indicate a breakdown of GR. Similar analysis is also performed for the DESI and Euclid surveys and compared to J-PAS with two configurations providing different areas, namely an initial expectation with 4000 deg2 and the future best case scenario with 8500 deg2. We show that J-PAS will be able to measure the parameters μ and η at a sensitivity of $2\!-\!7{{\ \rm per\ cent}}$, and will provide the best constraints in the interval z = 0.3–0.6, thanks to the large number of ELGs detectable in that redshift range. We also discuss the constraining power of J-PAS for dark energy models with a time-dependent equation-of-state parameter of the type w(a) = w0 + wa(1 − a), obtaining Δw0 = 0.058 and Δwa = 0.24 for the absolute errors of the dark energy parameters.

Optimising growth of structure constraints on modified gravity

We use growth of structure data to constrain the effective field theory of dark energy. Considering as case study Horndeski theories with the speed of gravitational waves equal to that of light, we show how constraints on the free parameters and the large-scale structure phenomenological functions can be improved by two ingredients: firstly by complementing the set of redshift-space distortions data with the three recent measurements of the growth rate f and the amplitude of matter fluctuations σ8 from the VIPERS and SDSS collaborations; secondly by applying a local Solar System bound on the variation of the Newton constant. This analysis allows us to conclude that: i) despite firmly restricting the predictions of weaker gravity, the inclusion of the Solar System bound does not prevent suppressed growth relative to the standard model ΛCDM at low redshifts; ii) the same bound in conjunction with the growth of structure data strongly restricts the redshift evolution of the gravitational slip parameter to be close to unity and the present value is constrained to one at the 10−3 level; iii) the growth of structure data favours a fifth force contribution to the effective gravitational coupling at low redshifts and at more than {two} sigma at present time.

Future constraints on the gravitational slip with the mass profiles of galaxy clusters

The gravitational slip parameter is an important discriminator between large classes of gravity theories at cosmological and astrophysical scales. In this work we use a combination of simulated information of galaxy cluster mass profiles, inferred by Strong+Weak lensing analyses and by the study of the dynamics of the cluster member galaxies, to reconstruct the gravitational slip parameter $\eta$ and predict the accuracy with which it can be constrained with current and future galaxy cluster surveys. Performing a full-likelihood statistical analysis, we show that galaxy cluster observations can constrain $\eta$ down to the percent level already with a few tens of clusters. We discuss the significance of possible systematics, and show that the cluster masses and numbers of galaxy members used to reconstruct the dynamics mass profile have a mild effect on the predicted constraints.

Dark energy survivals in massive gravity after GW170817: SO(3) invariant

The recent detection of the gravitational wave signal GW170817 together with an electromagnetic counterpart GRB 170817A from the merger of two neutron stars puts a stringent bound on the tensor propagation speed. This constraint can be automatically satisfied in the framework of massive gravity. In this work, we consider a general SO(3)-invariant massive gravity with five propagating degrees of freedom and derive the conditions for the absence of ghosts and Laplacian instabilities in the presence of a matter perfect fluid on the flat Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological background. The graviton potential containing the dependence of three-dimensional metrics and a fiducial metric coupled to a temporal scalar field gives rise to a scenario of the late-time cosmic acceleration in which the dark energy equation of state wDE is equivalent to −1 or varies in time. We find that the deviation from the value wDE=−1 provides important contributions to the quantities associated with the stability conditions of tensor, vector, and scalar perturbations. In concrete models, we study the dynamics of dark energy arising from the graviton potential and show that there exist viable parameter spaces in which neither ghosts nor Laplacian instabilities are present for both wDE>−1 and wDE<−1. We also generally obtain the effective gravitational coupling Geff with non-relativistic matter as well as the gravitational slip parameter ηs associated with the observations of large-scale structures and weak lensing. We show that, apart from a specific case, the two quantities Geff and ηs are similar to those in general relativity for scalar perturbations deep inside the sound horizon.

The VIMOS Public Extragalactic Redshift Survey (VIPERS)

We carry out a joint analysis of redshift-space distortions and galaxy-galaxy lensing, with the aim of measuring the growth rate of structure; this is a key quantity for understanding the nature of gravity on cosmological scales and late-time cosmic acceleration. We make use of the final VIPERS redshift survey dataset, which maps a portion of the Universe at a redshift of $z \simeq 0.8$, and the lensing data from the CFHTLenS survey over the same area of the sky. We build a consistent theoretical model that combines non-linear galaxy biasing and redshift-space distortion models, and confront it with observations. The two probes are combined in a Bayesian maximum likelihood analysis to determine the growth rate of structure at two redshifts $z=0.6$ and $z=0.86$. We obtain measurements of $f\sigma_8(0.6) = 0.48 \pm 0.12$ and $f\sigma_8(0.86) = 0.48 \pm 0.10$. The additional galaxy-galaxylensing constraint alleviates galaxy bias and $\sigma_8$ degeneracies, providing direct measurements of $[f(0.6),\sigma_8(0.6)] = [0.93 \pm 0.22, 0.52 \pm 0.06]$ and $f(0.86),\sigma_8(0.86)] = [0.99 \pm 0.19, 0.48 \pm 0.04]$. These measurements are statistically consistent with a Universe where the gravitational interactions can be described by General Relativity, although they are not yet accurate enough to rule out some commonly considered alternatives. Finally, as a complementary test we measure the gravitational slip parameter, $E_G$ , for the first time at $z>0.6$. We find values of $\smash{\overline{E}_G}(0.6) = 0.16 \pm 0.09$ and $\smash{\overline{E}_G}(0.86) = 0.09 \pm 0.07$, when $E_G$ is averaged over scales above $3 h^{-1} \rm{Mpc}$. We find that our $E_G$ measurements exhibit slightly lower values than expected for standard relativistic gravity in a {\Lambda}CDM background, although the results are consistent within $1-2\sigma$.

Diagnostic of Horndeski theories

We study the effects of Horndeski models of dark energy on the observables of the large-scale structure in the late time universe. A novel classification into Late dark energy, Early dark energy and Early modified gravity scenarios is proposed, according to whether such models predict deviations from the standard paradigm persistent at early time in the matter domination epoch. We discuss the physical imprints left by each specific class of models on the effective Newton constant μ, the gravitational slip parameter η, the light deflection parameter Σ and the growth function fσ8 and demonstrate that a convenient way to dress a complete portrait of the viability of the Horndeski accelerating mechanism is via two, redshift-dependent, diagnostics: the μ(z) − Σ(z) and the fσ8(z) − Σ(z) planes. If future, model-independent, measurements point to either Σ − 1 < 0 at redshift zero or μ − 1 < 0 with Σ − 1 > 0 at high redshifts or μ − 1 > 0 with Σ − 1 < 0 at high redshifts, Horndeski theories are effectively ruled out. If fσ8 is measured to be larger than expected in a ΛCDM model at z > 1.5 then Early dark energy models are definitely ruled out. On the opposite case, Late dark energy models are rejected by data if Σ < 1, while, if Σ > 1, only Early modifications of gravity provide a viable framework to interpret data.

Phenomenology of dark energy: general features of large-scale perturbations

We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to ΛCDM at intermediate redshifts (0.5 ≲ z ≲ 1), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by ΛCDM. (3) The gravitational slip parameter η—the ratio of the space part of the metric perturbation to the time part—is bounded from above. For Brans-Dicke-type theories η is at most unity. For more general theories, η can exceed unity at intermediate redshifts, but not more than about 1.5 if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.

Possibility of realizing weak gravity in redshift space distortion measurements

We study the possibility of realizing a growth rate of matter density perturbations lower than that in General Relativity. Using the approach of the effective field theory of modified gravity encompassing theories beyond Horndeski, we derive the effective gravitational coupling $G_{\rm eff}$ and the gravitational slip parameter $\eta$ for perturbations deep inside the Hubble radius. In Horndeski theories we derive a necessary condition for achieving weak gravity associated with tensor perturbations, but this is not a sufficient condition due to the presence of a scalar-matter interaction that always enhances $G_{\rm eff}$. Beyond the Horndeski domain it is possible to realize $G_{\rm eff}$ smaller than Newton's gravitational constant $G$, while the scalar and tensor perturbations satisfy no-ghost and stability conditions. We present a concrete dark energy scenario with varying $c_{\rm t}$ and numerically study the evolution of perturbations to confront the model with the observations of redshift-space distortions and weak lensing.

Higgs effective potential in a perturbed Robertson-Walker background

We calculate the one-loop effective potential of a scalar field in a Robertson-Walker background with scalar metric perturbations. A complete set of orthonormal solutions of the perturbed equations is obtained by using the adiabatic approximation for comoving observers. After analyzing the problem of renormalization in inhomogeneous backgrounds, we get the explicit contribution of metric perturbations to the effective potential. We apply these results to the Standard Model Higgs field and evaluate the effects of metric perturbations on the Higgs mass and on its vacuum expectation value. Space-time variations are found, which are proportional to the gravitational slip parameter, with a typical amplitude of the order of $\Delta\phi/\phi\simeq 10^{-11}$ on cosmological scales. We also discuss possible astrophysical signatures in the Solar System and in the Milky Way that could open new possibilities to explore the symmetry breaking sector of the electroweak interactions.

Structure formation in f(R) gravity: a distinguishing probe between the dark energyand modified gravity

In this work, we study the large scale structure formation in the modified gravity in the framework of Palatini formalism and compare the results with the equivalent smooth dark energy models as a tool to distinguish between these models. Through the inverse method, we reconstruct the dynamics of universe, modified gravity action and the structure formation indicators like the screened mass function and gravitational slip parameter. Consequently, we extract the matter density power spectrum for these two models in the linear regime and show that the modified gravity and dark energy models predictions are slightly different from each other at large scales. It is also shown that the growth index in the modified gravity unlike to the dark energy models is a scale dependent parameter. We also compare the results with those from the modified gravity in the metric formalism. The modification on the structure formation can also change the CMB spectrum at large scales however due to the cosmic variance it is hard to detect this signature. We show that a large number of SNIa data in the order of 2000 will enable us to reconstruct the modified gravity action with a suitable confidence level and test the cosmic acceleration models by the structure formation.