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The cosmological dynamics of gravitational clustering satisfies an approximate invariance with respect to the cosmological parameters that is often used to simplify analytical computations. We describe how this approximate symmetry gives rise to angular-averaged consistency relations for the matter density correlations. This allows one to write the (ℓ + n) density correlation, with ℓ large-scale linear wave numbers that are integrated over angles, and n fixed small-scale nonlinear wave numbers, in terms of the small-scale n-point density correlation and ℓ prefactors that involve the linear power spectra at the large-scale wave numbers. These relations, which do not vanish for equal-time statistics, go beyond the already known kinematic consistency relations. They could be used to detect primordial non-Gaussianities, modifications of gravity, limitations of galaxy biasing schemes, or to help design analytical models of gravitational clustering. [ABSTRACT FROM AUTHOR]

We study the predictions for the matter redshift-space power spectrum and correlation function of a Lagrangian-space Gaussian ansatz introduced in a previous work. This model is a natural extension of the Zeldovich approximation, where the displacement and velocity power spectra are determined by the equations of motion, instead of being set equal to the linear power spectrum. It does not contain any free parameter. As for the real-space statistics, we find that this Lagrangian-space approach is much more efficient for the correlation functions than for the power spectra. The damping of the baryon acoustic oscillations (BAO) oscillations is well recovered, but there is a large smooth drift from the simulations in the power spectra. The multipoles of the correlation functions are well recovered on BAO scales, with an accuracy of 2% for ξs0 down to 10h-1 Mpc, and of 3% for ξs2 down to 26h-1 Mpc, at z≥0.35. [ABSTRACT FROM AUTHOR]

We present a new approach to model the gravitational dynamics of large-scale structures. Instead of solving the equations of motion up to a finite perturbative order or building phenomenological models, we follow the evolution of the probability distribution of the displacement and velocity fields within an approximation subspace. Keeping the exact equations of motion with their full nonlinearity, this provides a nonperturbative scheme that goes beyond shell crossing. Focusing on the simplest case of a curl-free Gaussian Ansatz for the displacement and velocity fields, we find that truncations of the power spectra on nonlinear scales directly arise from the equations of motion. This leads to a truncated Zeldovich approximation for the density power spectrum, but with a truncation that is not set a priori and with different power spectra for the displacement and velocity fields. The positivity of their autopower spectra also follows from the equations of motion. Although the density power spectrum is only recovered up to a smooth drift on baryon acoustic oscillation (BAO) scales, the predicted density correlation function agrees with numerical simulations within 2% from BAO scales down to 7 h - 1 Mpc at z = 0.35, without any free parameter. Thus, this parameter-free extension of the Zeldovich approximation is not competitive with other schemes for the power spectrum, but it provides a good prediction for the correlation function. However, the improvement over the standard Zeldovich approximation remains rather modest. This means that including non-Gaussianities will be essential to significantly improve analytical predictions within this general framework. [ABSTRACT FROM AUTHOR]

We study the effects of screened modified gravity of the f(R), dilaton and symmetron types on structure formation, from the quasilinear to the nonlinear regime, using semianalytical methods. For such models, where the range of the new scalar field is typically within the Mpc range and below in the cosmological context, nonlinear techniques are required to understand the deviations of the power spectrum of the matter density contrast compared to the ΛCDM template. This is nowadays commonly tackled using extensive N-body simulations. Here we present new results combining exact perturbation theory at the one-loop level (and a partial resummation of the perturbative series) with a halo model. The former allows one to extend the linear perturbative analysis up to k 0.15h Mpc-1 at the perturbative level while the latter leads to a reasonable, up to a few percent, agreement with numerical simulations for k≲3h Mpc-1 for large-curvature f(R) models, and k≲1h Mpc-1 for dilatons and symmetrons, at z=0. We also discuss how the behaviors of the perturbative expansions and of the spherical collapse differ for f(R), dilaton, and symmetron models. [ABSTRACT FROM AUTHOR]

The clustering ratio η, a large-scale structure observable originally designed to constrain the shape of the power spectrum of matter density fluctuations, is shown to provide a sensitive probe of the nature of gravity in the cosmological regime. We apply this analysis to F(R) theories of gravity using the luminous red galaxy sample extracted from the spectroscopic Sloan Digital Sky Survey (SDSS) data release 7 and 10 catalogs. We find that general relativity (GR), complemented with a Friedmann-Robertson-Walker (FRW) cosmological model with parameters fixed by the Planck satellite, describes extremely well the clustering of galaxies up to z~0.6. On large cosmic scales, the absolute amplitude of deviations from GR, |fRo|, is constrained to be smaller than 4.6 × 10-5 at the 95% confidence level. This bound makes cosmological probes of gravity almost competitive with the sensitivity of Solar System tests, although still one 1 order of magnitude less effective than astrophysical tests. We also extrapolate our results to future large surveys like Euclid and show that the astrophysical bound will certainly remain out of reach for such a class of modified-gravity models that only differ from ACDM at low redshifts. [ABSTRACT FROM AUTHOR]