We perform theoretical and numerical studies of the full relativistic two-point galaxy correlation function, considering the linear-order scalar and tensor perturbation contributions and the wide-angle effects. Using the gauge-invariant relativistic description of galaxy clustering and accounting for the contributions at the observer position, we demonstrate that the complete theoretical expression is devoid of any long-mode contributions from scalar or tensor perturbations and it lacks the infrared divergences in agreement with the equivalence principle. By showing that the gravitational potential contribution to the correlation function converges in the infrared, our study justifies an IR cut-off $(k_{\text{IR}} \leq H_0)$ in computing the gravitational potential contribution. Using the full gauge-invariant expression, we numerically compute the galaxy two-point correlation function and study the individual contributions in the conformal Newtonian gauge. We find that the terms at the observer position such as the coordinate lapses and the observer velocity (missing in the standard formalism) dominate over the other relativistic contributions in the conformal Newtonian gauge such as the source velocity, the gravitational potential, the integrated Sachs-Wolf effect, the Shapiro time-delay and the lensing convergence. Compared to the standard Newtonian theoretical predictions that consider only the density fluctuation and redshift-space distortions, the relativistic effects in galaxy clustering result in a few percent-level systematic errors beyond the scale of the baryonic acoustic oscillation. Our theoretical and numerical study provides a comprehensive understanding of the relativistic effects in the galaxy two-point correlation function, as it proves the validity of the theoretical prediction and accounts for effects that are often neglected in its numerical evaluation.
We study wide-angle correlations in the galaxy power spectrum in redshift space, including all general relativistic effects and the Kaiser Rocket effect in general relativity. We find that the Kaiser Rocket effect becomes important on large scales and at high redshifts, and leads to new contributions in wide-angle correlations. We believe this effect might be very important for future large volume surveys.
We present a systematic study of galaxy bias in the presence of primordial non-Gaussianity in General Relativity (GR) at second order in perturbation theory. The non-linearity of the Poisson equation in GR and primordial non-Gaussianity are consistently included. We show that the inclusion of non-local primordial non-Gaussianity in addition to local non-Gaussianity is important to show the absence of the modulation of small scale clustering by the long-wavelength mode in the single field slow-roll inflation. We study the bispectrum of the relativistic galaxy density in several gauges and ident…
We compute the second-order density fluctuation in the proper-time hypersurface of non-relativistic matter flows and relate it to the galaxy number density fluctuation in general relativity. At the linear order, it is equivalent to the density fluctuation in the comoving synchronous gauge, in which two separate gauge conditions coincide. However, at the second order, the density fluctuations in these gauge conditions differ, while both gauge conditions represent the proper-time hypersurface. Compared to the density fluctuation in the temporal comoving and the spatial C-gauge conditions, the de…
We discuss the question of gauge choice when analysing relativistic density perturbations at second order. We compare Newtonian and General Relativistic approaches. Some misconceptions in the recent literature are addressed. We show that the comoving-synchronous gauge is the unique gauge in General Relativity that corresponds to the Lagrangian frame and is entirely appropriate to describe the matter overdensity at second order. The comoving-synchronous gauge is the simplest gauge in which to describe Lagrangian bias at second order.
Deviations from general relativity in order to explain cosmic acceleration generically have both time and scale dependent signatures in cosmological data. We extend our previous work by investigating model independent gravitational deviations in bins of redshift and length scale, by incorporating further cosmological probes such as temperature-galaxy and galaxy-galaxy cross-correlations, and by examining correlations between deviations. Markov Chain Monte Carlo likelihood analysis of the model independent parameters fitting current data indicates that at low redshift general relativity deviate…
We review our contribution to infrared Renormalization Group (RG) effects to General Relativity in the context of galaxies. Considering the effective action approach to Quantum Field Theory in curved background, we argued that the proper RG energy scale, in the weak field limit, should be related to the Newtonian potential. In the galaxy context, even without dark matter, this led to a remarkably small gravitational coupling G variation (about or less than 10^{-12} of its value per light-year), while also capable of generating galaxy rotation curves about as good as the best phenomenological d…
Nowadays, thanks to the improved precision of cosmological data, it has been possible to search for deviation from the general relativity theory with tests on large cosmic scales. Particularly, there is a class of modified gravity theories that breaks the Einstein equivalence principle (EEP) in the electromagnetic sector, generating variations of the fine structure constant, violations of the cosmic distance duality relation and the evolution law of the cosmic microwave background (CMB) radiation. In recent papers, this class of theories has been tested with angular diameter distances from gal…
Although general relativity underlies modern cosmology, its applicability on cosmological length scales has yet to be stringently tested. Such a test has recently been proposed, using a quantity, EG, that combines measures of large-scale gravitational lensing, galaxy clustering and structure growth rate. The combination is insensitive to 'galaxy bias' (the difference between the clustering of visible galaxies and invisible dark matter) and is thus robust to the uncertainty in this parameter. Modified theories of gravity generally predict values of EG different from the general relativistic pre…
We compute the real space galaxy power spectrum, including the leading order effects of General Relativity and primordial non-Gaussianity from the $f_{\mathrm{NL}}$ and $g_{\mathrm{NL}}$ parameters. Such contributions come from the one-loop matter power spectrum terms dominant at large scales, and from the factors of the non-linear bias parameter $b_{\mathrm{NL}}$ (akin to the Newtonian $b_ϕ$). We assess the detectability of these contributions in Stage-IV surveys. In particular, we note that specific values of the bias parameter may erase the primordial and relativistic contributions to the c…
Observations of galaxy-scale strong gravitational lensing (SGL) systems have enabled unique tests of nonlinear departures from general relativity (GR) on the galactic and supergalactic scales. One of the most important cases of such tests is constraints on the gravitational slip between two scalar gravitational potentials. In this paper, we use a newly compiled sample of strong gravitational lenses to test the validity of GR, focusing on the screening effects on the apparent positions of lensed sources relative to the GR predictions. This is the first simultaneous measurement of the Post-Newto…
We use galaxy-galaxy weak lensing data to perform a novel test on general relativity (GR) and $f(T)$ torsional gravity. In particular, we impose strong constraints using the torsional (teleparallel) formulation of gravity in which the deviation from GR is quantified by a single parameter $α$, an approximation which is always valid at low-redshift Universe and weak gravitational fields. We calculate the difference in the deflection angle and eventually derive the modified excess surface density profile, which is mainly affected at small scales. Confronting the predictions with weak lensing data…
We present the galaxy power spectrum in general relativity. Using a novel approach, we derive the galaxy power spectrum taking into account all the relativistic effects in observations. In particular, we show independently of survey geometry that relativistic effects yield no divergent terms (proportional to $k^{-4}P_m(k)$ or $k^{-2}P_m(k)$ on all scales) that would mimic the signal of primordial non-Gaussianity. This cancellation of such divergent terms is indeed expected from the equivalence principle, meaning that any perturbation acting as a uniform gravity on the scale of the experiment c…
The proper general relativistic description of the observed galaxy power spectrum is substantially different from the standard Newtonian description on large scales, providing a unique opportunity to test general relativity on horizon scales. Using the Einstein equations, the general relativistic effects can be classified as two new terms that represent the velocity and the gravitational potential, coupling to the time evolution of galaxy number density and Hubble parameter. Compared to the dominant density and velocity redshift-space distortion terms, the former scales as H/k and correlates t…
The accelerating expansion of the Universe at recent epochs has called into question the validity of general relativity on cosmological scales. One probe of gravity is a comparison of expansion history of the Universe with the history of structure growth via gravitational instability: general relativity predicts a specific relation between these two observables. Here we show that the mean pairwise streaming velocity of galaxy clusters provides a useful method of constraining this relation. Galaxy cluster velocities can be measured via the kinetic Sunyaev-Zeldovich distortion of the cosmic micr…
The apparent sizes and brightnesses of galaxies are correlated in a dipolar pattern around matter overdensities in redshift space, appearing larger on their near side and smaller on their far side. The opposite effect occurs for galaxies around an underdense region. These patterns of apparent magnification induce dipole and higher multipole terms in the cross-correlation of galaxy number density fluctuations with galaxy size/brightness (which is sensitive to the convergence field). This provides a means of directly measuring peculiar velocity statistics at low and intermediate redshift, with s…
The testing of general relativity at cosmological scales has become a possible and timely endeavor that is not only motivated by the pressing question of cosmic acceleration but also by the proposals of some extensions to general relativity that would manifest themselves at large scales of distance. We analyze here correlations between modified gravity growth parameters and some core cosmological parameters using the latest cosmological data sets including the refined Cosmic Evolution Survey 3D weak lensing. We provide parametrized modified growth equations and their evolution. We implement kn…
Although general relativity (GR) has been precisely tested at the solar system scale, precise tests at a galactic or cosmological scale are still relatively insufficient. Here, in order to test GR at the galactic scale, we use the newly compiled galaxy-scale strong gravitational lensing (SGL) sample to constrain the parameter $γ_{PPN}$ in the parametrized post-Newtonian (PPN) formalism. We employ the Pantheon sample of type Ia supernovae observation to calibrate the distances in the SGL systems using the Gaussian Process method, which avoids the logical problem caused by assuming a cosmologica…
This is the third of a series of papers in which we derive simultaneous constraints on cosmological parameters and X-ray scaling relations using observations of the growth of massive, X-ray flux-selected galaxy clusters. Our data set consists of 238 clusters drawn from the ROSAT All-Sky Survey, and incorporates extensive follow-up observations using the Chandra X-ray Observatory. Here we present improved constraints on departures from General Relativity (GR) on cosmological scales, using the growth index, gamma, to parameterize the linear growth rate of cosmic structure. Using the method of Ma…
Thus far, there does not appear to be an agreed (or adequate) definition of homogeneous dark energy (DE). This paper seeks to define a valid, adequate homogeneity condition for DE. Firstly, it is shown that as long as $w_x \neq -1$, DE must have perturbations. It is then argued, independent of $w_x$, that a correct definition of homogeneous DE is one whose density perturbation vanishes in comoving gauge: and hence, in the DE rest frame. Using phenomenological DE, the consequence of this approach is then investigated in the observed galaxy power spectrum - with the power spectrum being normaliz…
We consider the application of quantum corrections computed using renormalization group arguments in the astrophysical domain and show that, for the most natural interpretation of the renormalization group scale parameter, a gravitational coupling parameter $G$ varying $10^{-7}$ of its value across a galaxy (which is roughly a variation of $10^{-12}$ per light-year) is sufficient to generate galaxy rotation curves in agreement with the observations. The quality of the resulting fit is similar to the Isothermal profile quality once both the shape of the rotation curve and the mass-to-light rati…
If the accelerated expansion of the universe is due to a modification of general relativity at late times, it is likely that the growth of structure on large scales would also display deviations from the standard cosmology. We investigate the statistics of the distribution of galaxy cluster-sized halos as a probe of gravity. We analyze the output of several matched N-body simulations with the same initial conditions and expansion histories but using both DGP and f (R) gravity with various parameters. From each simulation we extract the cluster mass function, power spectrum, and mean pairwise v…
The peculiar velocity distribution of cluster member galaxies provides a powerful tool to directly investigate the gravitational potentials within galaxy clusters and to test the gravity theory on megaparsec scales. We exploit spectroscopic galaxy and galaxy cluster samples extracted from the latest releases of the Sloan Digital Sky Survey (SDSS) to derive new constraints on the gravity theory. We consider a spectroscopic sample of $3058$ galaxy clusters, with a maximum redshift of $0.5$. We analyse the velocity distribution of the cluster member galaxies to make new measurements of the gravit…
We extend previous analyses of wide-angle correlations in the galaxy power spectrum in redshift space to include all general relativistic effects. These general relativistic corrections to the standard approach become important on large scales and at high redshifts, and they lead to new terms in the wide-angle correlations. We show that in principle the new terms can produce corrections of nearly 10 % on Gpc scales over the usual Newtonian approximation. General relativistic corrections will be important for future large-volume surveys such as SKA and Euclid, although the problem of cosmic var…
Several recent studies have shown how to properly calculate the observed clustering of galaxies in a relativistic context, and uncovered corrections to the Newtonian calculation that become significant on scales near the horizon. Here, we retrace these calculations and show that, on scales approaching the horizon, the observed galaxy power spectrum depends strongly on which gauge is assumed to relate the intrinsic fluctuations in galaxy density to matter perturbations through a linear bias relation. Starting from simple physical assumptions, we derive a gauge-invariant expression relating gala…
We measure a combination of gravitational lensing, galaxy clustering, and redshift-space distortions called $E_G$. The quantity $E_G$ probes both parts of metric potential and is insensitive to galaxy bias and $σ_8$. These properties make it an attractive statistic to test $Λ$CDM, General Relativity and its alternate theories. We have combined CMASS DR11 with CFHTLenS and recent measurements of $β$ from RSD analysis, and find $E_G(z = 0.57) = 0.42 \pm 0.056$, an 13\% measurement in agreement with the prediction of general relativity $E_G(z = 0.57) = 0.396 \pm 0.011$ using the Planck 2015 cosmo…
The general relativistic description of galaxy clustering provides a complete and unified treatment of all the effects in galaxy clustering such as the redshift-space distortion, gravitational lensing, Sachs-Wolfe effects, and their relativistic effects. In particular, the relativistic description resolves the gauge issues in the standard Newtonian description of galaxy clustering by providing the gauge-invariant expression for the observed galaxy number density. The relativistic effect in galaxy clustering is significant on large scales, in which dark energy models or alternative theories of …
Wojtak, Hansen and Hjorth have recently claimed to confirm general relativity and to rule out the tensor-vector-scalar (TeVeS) gravitational theory based on an analysis of the gravitational redshifts of galaxies in 7800 clusters. But their ubiquitous modeling of the sources of cluster gravitational fields with Navarro-Frenk-White mass profiles is neither empirically justified out to the necessary radii in clusters, nor germane in the case of TeVeS. Using MONDian isothermal sphere models consistently constructed within MOND (equivalent to TeVeS models), we can fit the determined redshifts no wo…
Extended Theories of Gravity with additional scalar degrees of freedom have recently acquired increasing interest due to the presence of a screening mechanism that allows suppressing at small scales (e.g., the Solar System scale) every modification restoring General Relativity. In this work, we consider a second-order Extended Theory of Gravity belonging to the family of Degenerate High Order Scalar Tensor theories (DHOST) characterized by a partial breaking of the Vainshtein screening mechanism. We study this model in two different scenarios as a description of dark energy only and as a descr…
We assess the effect of magnification bias on the $E_G$ statistic for probing gravity. $E_G$, a statistic constructed from power spectrum estimates of both weak lensing and redshift space distortions (RSD), directly tests general relativity (GR) while in principle being independent of clustering bias. This property has motivated its recent use in multiple tests of GR. Recent work has suggested that the magnification bias of galaxies due to foreground matter perturbations breaks the bias-independence of the $E_G$ statistic. The magnitude of this effect is very sensitive to the clustering and ma…
The morphological properties of large scale structure of the Universe can be fully described by four Minkowski functionals (MFs), which provide important complementary information to other statistical observables such as the widely used 2-point statistics in configuration and Fourier spaces. In this work, for the first time, we present the differences in the morphology of large scale structure caused by modifications to general relativity (to address the cosmic acceleration problem), by measuring the MFs from N-body simulations of modified gravity and general relativity. We find strong statist…
We present constraints on testing general relativity (GR) at cosmological scales using recent data sets and assess the impact of galaxy intrinsic alignment (IA) in the CFHTLenS lensing data on those constraints. We consider CMB temperature data from Planck, the galaxy power spectrum from WiggleZ, weak lensing tomography from the CFHTLenS, ISW-galaxy cross correlations, and BAO data from 6dF, SDSS DR7, and BOSS DR9. We use a parameterization of the modified gravity (MG) that is binned in redshift and scale, a parameterization that evolves monotonically in scale but is binned in redshift, and a …
We investigate the correlation between the distribution of galaxies and the predicted gravitational-wave background of astrophysical origin. We show that the large angular scale anisotropies of this background are dominated by nearby non-linear structure, which depends on the notoriously hard to model galaxy power spectrum at small scales. In contrast, we report that the cross-correlation of this signal with galaxy catalogues depends only on linear scales and can be used to constrain the average contribution to the gravitational-wave background as a function of time. Using mock data based on a…
We discover a linear relation between two sets of galaxy-lensing cross-correlations. This linear relation holds, as long as light follows the geodesic and the metric is Friedmann-Lemaître-Robertson-Walker (FLRW). Violation of the cosmological principle (and equivalently the FLRW metric) will break this linear relation. Therefore it provides a powerful test of the cosmological principle, based on direct observables and relied on no specific cosmological models. We demonstrate that stage IV galaxy surveys and CMB-S4 experiments will be able to test this linear relation stringently and therefore …
Assuming a LCDM universe in a single-field inflationary scenario, we compute the three-point correlation function of the observed matter density fluctuation in the squeezed triangular configuration, accounting for all the relativistic effects at the second order in perturbations. This squeezed three-point correlation function characterizes the local-type primordial non-Gaussianity, and it has been extensively debated in literature whether there exists a prominent feature in galaxy clustering on large scales in a single-field inflationary scenario either from the primordial origin or the intrin…
Forthcoming projects such as the DES, a JDEM, and LSST, aim to measure weak lensing shear correlations with unprecedented accuracy. Weak lensing observables are sensitive to both the distance-redshift relation and the growth of structure in the Universe. If the cause of accelerated cosmic expansion is dark energy within general relativity (GR), both cosmic distances and structure growth are governed by the properties of dark energy. Consequently, one may use lensing to check for this consistency and test GR. After reviewing the phenomenology of such tests, we address one major challenge to suc…
We calculate the relativistic corrections to hydrostatic X-ray masses for galaxy clusters in Kottler spacetime, which is the spherically symmetric solution to Einstein's equations in General relativity endowed with a cosmological constant. The hydrostatic masses for clusters (calculated assuming Newtonian gravity) have been found to be underestimated compared to lensing masses, and this discrepancy is known as hydrostatic mass bias. Since the relativistic hydrostatic X-ray masses are automatically lower than lensing masses, under the edifice of Kottler metric, we check if the hydrostatic mass …
Modified gravity theories with a screening mechanism have acquired much interest recently in the quest for a viable alternative to General Relativity on cosmological scales, given their intrinsic property of being able to pass Solar System scale tests and, at the same time, to possibly drive universe acceleration on much larger scales. Here, we explore the possibility that the same screening mechanism, or its breaking at a certain astrophysical scale, might be responsible of those gravitational effects which, in the context of general relativity, are generally attributed to Dark Matter. We con…
General Relativity (GR) has been successfully tested mainly at Solar system scales; however, galaxy-scale tests have become popular in the last few decades. In this work, we investigate the $η_\text{PPN}$ parameter, which is commonly defined by the ratio of two scalar potentials that appears in the cosmological linearly perturbed metric. Under the assumption of GR and a vanish anisotropic stress tensor, $η_\text{PPN}= 1$. Using ALMA, HST, and VLT/MUSE data, we combine mass measurements, using gravitational lensing and galactic dynamics, for the SDP.81 lens galaxy ($z = 0.299$) to constrain $η_…
We propose a novel method to measure the $E_G$ statistic from clustering alone. The $E_G$ statistic provides an elegant way of testing the consistency of General Relativity by comparing the geometry of the Universe, probed through gravitational lensing, with the motion of galaxies in that geometry. Current $E_G$ estimators combine galaxy clustering with gravitational lensing, measured either from cosmic shear or from CMB lensing. In this paper, we construct a novel estimator for $E_G$, using only clustering information obtained from two tracers of the large-scale structure: intensity mapping a…
The physics of gravity on cosmological scales affects both the rate of assembly of large-scale structure, and the gravitational lensing of background light through this cosmic web. By comparing the amplitude of these different observational signatures, we can construct tests that can distinguish general relativity from its potential modifications. We used the latest weak gravitational lensing dataset from the Kilo-Degree Survey, KiDS-1000, in conjunction with overlapping galaxy spectroscopic redshift surveys BOSS and 2dFLenS, to perform the most precise existing amplitude-ratio test. We measur…
Length scales probed by large scale structure surveys are becoming closer to the horizon scale. Further, it has been recently understood that non-Gaussianity in the initial conditions could show up in a scale dependence of the bias of galaxies at the largest distances. It is therefore important to include General Relativistic effects. Here we provide a General Relativistic generalization of the bias, valid both for Gaussian and non-Gaussian initial conditions. The collapse of objects happens on very small scales, while long-wavelength modes are always in the quasi linear regime. Around every c…
We study the impact of lensing corrections on modeling cross correlations between CMB lensing and galaxies, cosmic shear and galaxies, and galaxies in different redshift bins. Estimating the importance of these corrections becomes necessary in the light of anticipated high-accuracy measurements of these observables. While higher order lensing corrections (sometimes also referred to as post Born corrections) have been shown to be negligibly small for lensing auto correlations, they have not been studied for cross correlations. We evaluate the contributing four-point functions without making use…
We present a new test of gravitational physics by comparing the growth rate of cosmic structure measured around voids with that measured around galaxies in the same large-scale structure dataset, the low-redshift 6-degree Field Galaxy Survey. By fitting a self-consistent Redshift Space Distortion model to the 2D galaxy-galaxy and void-galaxy correlation functions, we recover growth rate values fσ_8 = 0.42 \pm 0.06 and 0.39 \pm 0.11, respectively. The environmental-dependence of cosmological statistics can potentially discriminate between modified-gravity scenarios which modulate the growth rat…
The paper is about possible effects of infrared quantum contributions to General Relativity on disk and elliptical galaxies. The Renormalization Group corrected General Relativity (RGGR model) is used to parametrize these quantum effects. The new RGGR results presented here concern the elliptical galaxy NGC 4374 and the dwarf disk galaxy DDO 47. Using the effective approach to Quantum Field Theory in curved background, one can argue that the proper RG energy scale, in the weak field limit, should be related to the Newtonian potential. In the context of galaxies, this led to a remarkably small …
The Beyond Horndeski class of alternative gravity theories allow for Self-accelerating de-Sitter cosmologies with no need for a cosmological constant. This makes them viable alternatives to $Λ$CDM and so testing their small-scale predictions against General Relativity is of paramount importance. These theories generically predict deviations in both the Newtonian force law and the gravitational lensing of light inside extended objects. Therefore, by simultaneously fitting the X-ray and lensing profiles of galaxy clusters new constraints can be obtained. In this work, we apply this methodology t…
We investigate the use of the cross-correlation between galaxies and galaxy groups to measure redshift-space distortions (RSD) and thus probe the growth rate of cosmological structure. This is compared to the classical approach based on using galaxy auto-correlation. We make use of realistic simulated galaxy catalogues that have been constructed by populating simulated dark matter haloes with galaxies through halo occupation prescriptions. We adapt the classical RSD dispersion model to the case of the group-galaxy cross-correlation function and estimate the RSD parameter $β$ by fitting both th…
We present measurements of angular cross power spectra between galaxies and optically-selected galaxy clusters in the final photometric sample of the Sloan Digital Sky Survey (SDSS). We measure the auto- and cross-correlations between galaxy and cluster samples, from which we extract the effective biases and study the shot noise properties. We model the non-Poissonian shot noise by introducing an effective number density of tracers and fit for this quantity. We find that we can only describe the cross-correlation of galaxies and galaxy clusters, as well as the auto-correlation of galaxy cluste…
We present results from cross-correlating Planck CMB lensing maps with the Sloan Digital Sky Survey (SDSS) galaxy lensing shape catalog and BOSS galaxy catalogs. For galaxy position vs. CMB lensing cross-correlations, we measure the convergence signal around the galaxies in configuration space, using the BOSS LOWZ ($z\sim0.30$) and CMASS ($z\sim0.57$) samples. With fixed Planck 2015 cosmology, doing a joint fit with the galaxy clustering measurement, for the LOWZ (CMASS) sample we find a galaxy bias $b_g=1.75\pm0.04$ ($1.95\pm 0.02$) and galaxy-matter cross-correlation coefficient $r_{cc}=1.0\…
