Cosmic velocity-gravity relation in redshift space

We propose a simple way to estimate the parameter beta similar or equal to Omega(0.6)/b from 3D galaxy surveys, where Omega is the non-relativistic matter-density parameter of the Universe and b is the bias between the galaxy distribution and the total matter distribution. 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 = root 1 + 6 beta/5 + 3 beta(2)/7 / 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 non-linear 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 non-linear dynamics. Applications of the method to real galaxy catalogues are discussed, including a preliminary investigation on homogeneous (volume-limited) 'galaxy' samples extracted from the simulation with simple prescriptions based on halo and substructure identification, to quantify the effects of the bias between the galaxy distribution and the total matter distribution, as well as the effects of shot noise.