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Associating the formation sites of haloes with the maxima of the smoothed linear density field, we present nonperturbative predictions for the Lagrangian and evolved halo correlation functions that are valid at all separations. In Lagrangian space, we find significant deviations from the perturbative bias calculation at small scales, in particular, a pronounced exclusion region where ξ = - 1 for maxima of unequal height. Our predictions are in good agreement with the Lagrangian clustering of dark matter proto-haloes reconstructed from N-body simulations. Our predictions for the mean infall and velocity dispersion of haloes, which differ from the local bias expansion, show a similar level of agreement with simulations. Finally, we displace the initial density peaks according to the Zeldovich approximation in order to predict the late-time clustering of dark matter haloes. While we are able to reproduce the early evolution of this conserved set of tracers, our approximation fails at the collapse epoch (z=0) on nonlinear scales r ≲ 10 h-1     Mpc, emphasizing the need for a nonperturbative treatment of the halo displacement field. [ABSTRACT FROM AUTHOR]

In the peak approach, the formation sites of observable structures in the Universe are identified as peaks in the matter density field. The statistical properties of the clustering of peaks are particularly important in this respect. In this paper, we investigate the large-separation expansion of the correlation function of peaks in Gaussian random fields. The analytic formula up to third order is derived, and the resultant expression can be evaluated by a combination of one-dimensional fast Fourier transforms, which are evaluated very fast. The analytic formula obtained perturbatively in the large-separation limit is compared with a method of Monte Carlo integrations, and a complementarity between the two methods is demonstrated. [ABSTRACT FROM AUTHOR]

The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre transform of a function directly built in terms of the initial moments. In the context of the upcoming generation of large-scale structure surveys, it is conjectured that this result correctly models such a function for finite values of the variance. Detailed consequences of this assumption are explored. In particular the corresponding one-cell density probability distribution at finite variance is computed for realistic power spectra, taking into account its scale variation. It is found to be in agreement with A-cold dark matter simulations at the few percent level for a wide range of density values and parameters. Related explicit analytic expansions at the low and high density tails are given. The conditional (at fixed density) and marginal probability of the slope--the density difference between adjacent cells--and its fluctuations is also computed from the two-cell joint PDF; it also compares very well to simulations. It is emphasized that this could prove useful when studying the statistical properties of voids as it can serve as a statistical indicator to test gravity models and/or probe key cosmological parameters. [ABSTRACT FROM AUTHOR]

We present a specific prescription for the calculation of cosmological power spectra, exploited here at two-loop order in perturbation theory, based on the multipoint propagator expansion. In this approach, density and velocity power spectra are constructed from the regularized expressions of the propagators that reproduce both the resummed behavior in the high-k limit and the standard perturbation theory results at low k. With the help of N-body simulations, we particularly focus on the density field, and show that such a construction gives robust and accurate predictions for both the density power spectrum and the correlation function at percent level in the weakly nonlinear regime. We then present an algorithm that allows accelerated evaluations of all the required diagrams by reducing the computational tasks to one-dimensional integrals. This is achieved by means of precomputed kernel sets defined for appropriately chosen fiducial models. The computational time for two-loop results is then reduced from a few minutes, with the direct method, to a few seconds with the fast one. The robustness and applicability of this method are tested against the power spectrum COSMIC EMULATOR from which a wide variety of cosmological models can be explored. The FORTRAN PROGRAM with which direct and fast calculations of density power spectra can be done, REGPT, is publicly released as part of this paper. [ABSTRACT FROM AUTHOR]