Cosmic velocity--gravity relation in redshift space

Abstract

We propose a simple way to estimate the parameter beta = Omega_m^(0.6)/b from three-dimensional galaxy surveys. Our method consists in measuring the relation between the cosmological velocity and gravity fields, and thus requires peculiar velocity measurements. The relation is measured *directly in redshift space*, so there is no need to reconstruct the density field in real space. In linear theory, the radial components of the gravity and velocity fields in redshift space are expected to be tightly correlated, with a slope given, in the distant observer approximation, by g / v = (1 + 6 beta / 5 + 3 beta^2 / 7)^(1/2) / beta. We test extensively this relation using controlled numerical experiments based on a cosmological N-body simulation. To perform the measurements, we propose a new and rather simple adaptive interpolation scheme to estimate the velocity and the gravity field on a grid. One of the most striking results is that nonlinear effects, including `fingers of God', affect mainly the tails of the joint probability distribution function (PDF) of the velocity and gravity field: the 1--1.5 sigma region around the maximum of the PDF is *dominated by the linear theory regime*, both in real and redshift space. This is understood explicitly by using the spherical collapse model as a proxy of nonlinear dynamics. Applications of the method to real galaxy catalogs are discussed, including a preliminary investigation on homogeneous (volume limited) `galaxy' samples extracted from the simulation with simple prescriptions based on halo and sub-structure identification, to quantify the effects of the bias between the galaxy and the total matter distibution, and of shot noise (ABRIDGED).