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We show how the non-linearity of general relativity generates a characteristic non-Gaussian signal in cosmological large-scale structure that we calculate at all perturbative orders in a large scale limit. Newtonian gravity and general relativity provide complementary theoretical frameworks for modelling large-scale structure in $Lambda$CDM cosmology; a relativistic approach is essential to determine initial conditions which can then be used in Newtonian simulations studying the non-linear evolution of the matter density. Most inflationary models in the very early universe predict an almost Gaussian distribution for the primordial metric perturbation, $zeta$. However, we argue that it is the Ricci curvature of comoving-orthogonal spatial hypersurfaces, $R$, that drives structure formation at large scales. We show how the non-linear relation between the spatial curvature, $R$, and the metric perturbation, $zeta$, translates into a specific non-Gaussian contribution to the initial comoving matter density that we calculate for the simple case of an initially Gaussian $zeta$. Our analysis shows the non-linear signature of Einsteins gravity in large-scale structure.
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In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the dark matter density field on large scales - even if the primordial metric perturbation is Gaussian. Intrinsic non-Gaussianity in the large-scale dark matter overdensity in GR is real and physical. However, the variance smoothed on a local physical scale is not correlated with the large-scale curvature perturbation, so that there is no relativistic signature in the galaxy bias when using the simplest model of bias. It is an open question whether the observable mass proxies such as luminosity or weak lensing correspond directly to the physical mass in the simple halo bias model. If not, there may be observables that encode this relativistic signature.
Probes of cosmic expansion constitute the main basis for arguments to support or refute a possible apparent acceleration due to different expansion rates in the universe as described by inhomogeneous cosmological models. We present in this Letter a separate argument based on results from an analysis of the growth rate of large-scale structure in the universe as modeled by the inhomogeneous cosmological models of Szekeres. We use the models with no assumptions of spherical or axial symmetries. We find that while the Szekeres models can fit very well the observed expansion history without a $Lambda$, they fail to produce the observed late-time suppression in the growth unless $Lambda$ is added to the dynamics. A simultaneous fit to the supernova and growth factor data shows that the cold dark matter model with a cosmological constant ($Lambda$CDM) provides consistency with the data at a confidence level of 99.65% while the Szekeres model without $Lambda$ achieves only a 60.46% level. When the data sets are considered separately, the Szekeres with no $Lambda$ fits the supernova data as well as the $Lambda$CDM does, but provides a very poor fit to the growth data with only 31.31% consistency level compared to 99.99% for the $Lambda$CDM. This absence of late-time growth suppression in inhomogeneous models without a $Lambda$ is consolidated by a physical explanation.
The recent measurement of the gravitational redshifts of galaxies in galaxy clusters by Wojtak et al. has opened a new observational window on dark matter and modified gravity. By stacking clusters this determination effectively used the line of sight distortion of the cross-correlation function of massive galaxies and lower mass galaxies to estimate the gravitational redshift profile of clusters out to 4 Mpc/h. Here we use a halo model of clustering to predict the distortion due to gravitational redshifts of the cross-correlation function on scales from 1 - 100 Mpc/h. We compare our predictions to simulations and use the simulations to make mock catalogues relevant to current and future galaxy redshift surveys. Without formulating an optimal estimator, we find that the full BOSS survey should be able to detect gravitational redshifts from large-scale structure at the ~4 sigma level. Upcoming redshift surveys will greatly increase the number of galaxies useable in such studies and the BigBOSS and Euclid experiments should be capable of measurements with precision at the few percent level. As has been recently pointed out by McDonald, Kaiser and Zhao et al, other interesting effects including relativistic beaming and transverse Doppler shift can add additional asymmetric distortions to the correlation function. While these contributions are subdominant to the gravitational redshift on large scales, they represent additional opportunities to probe gravitational physics and indicate that many qualitatively new measurements should soon be possible using large redshift surveys.
Consistency between cosmological data sets is essential for ongoing and future cosmological analyses. We first investigate the questions of stability and applicability of some moment-based inconsistency measures to multiple data sets. We show that the recently introduced index of inconsistency (IOI) is numerically stable while it can be applied to multiple data sets. We use an illustrative construction of constraints as well as an example with real data sets (i.e. WMAP versus Planck) to show some limitations of the application of the Karhunen-Loeve decomposition to discordance measures. Second, we perform various consistency analyzes using IOI between multiple current data sets while textit{working with the entire common parameter spaces}. We find current Large-Scale-Structure (LSS) data sets (Planck CMB lensing, DES lensing-clustering and SDSS RSD) all to be consistent with one another. This is found to be not the case for Planck temperature (TT) versus polarization (TE,EE) data, where moderate inconsistencies are present. Noteworthy, we find a strong inconsistency between joint LSS probes and Planck with IOI=5.27, and a moderate tension between DES and Planck with IOI=3.14. Next, using the IOI metric, we compare the Hubble constant from five independent probes. We confirm previous strong tensions between local measurement (SH0ES) and Planck as well as between H0LiCOW and Planck, but also find new strong tensions between SH0ES measurement and the joint LSS probes with IOI=6.73 (i.e. 3.7-$sigma$ in 1D) as well as between joint LSS and combined probes SH0ES+H0LiCOW with IOI=8.59 (i.e. 4.1-$sigma$ in 1D). Whether due to systematic effects in the data sets or problems with the underlying model, sources of these old and new tensions need to be identified and dealt with.
The precision of the cosmological data allows us to accurately approximate the predictions for cosmological observables by Taylor expanding up to a low order the dependence on the cosmological parameters around a reference cosmology. By applying this observation to the redshift-space one-loop galaxy power spectrum of the Effective Field Theory of Large-Scale Structure, we analyze the BOSS DR12 data by scanning over all the parameters of $Lambda$CDM cosmology with massive neutrinos. We impose several sets of priors, the widest of which is just a Big Bang Nucleosynthesis prior on the current fractional energy density of baryons, $Omega_b h^2$, and a bound on the sum of neutrino masses to be less than 0.9 eV. In this case we measure the primordial amplitude of the power spectrum, $A_s$, the abundance of matter, $Omega_m$, the Hubble parameter, $H_0$, and the tilt of the primordial power spectrum, $n_s$, to about $19%$, $5.7%$, $2.2%$ and $7.3%$ respectively, obtaining $ln ( 10^{10} A_s) =2.91pm 0.19$, $Omega_m=0.314pm 0.018$, $H_0=68.7pm 1.5$ km/(s Mpc) and $n_s=0.979pm 0.071$ at $68%$ confidence level. A public code is released with this preprint.
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