Evolution mapping – II. Describing statistics of the non-linear cosmic velocity field

ABSTRACT We extend the evolution–mapping approach, introduced in the first paper of this series to describe non-linear matter density fluctuations, to statistics of the cosmic velocity field. This framework classifies cosmological parameters into shape parameters, which determine the shape of the linear matter power spectrum, $P_{\rm L}(k, z)$, and evolution parameters, which control its amplitude at any redshift. Evolution–mapping leverages the fact that density fluctuations in cosmologies with identical shape parameters but different evolution parameters exhibit similar non-linear evolutions when expressed as a function of clustering amplitude. We analyse a suite of N-body simulations sharing identical shape parameters but spanning a wide range of evolution parameters. Using a method for estimating the volume-weighted velocity field based on the Voronoi tessellation of simulation particles, we study the non-linear evolution of the velocity divergence power spectrum, $P_{\theta \theta }(k)$, and its cross-power spectrum with the density field, $P_{\delta \theta }(k)$. We demonstrate that the evolution–mapping relation applies accurately to $P_{\theta \theta }(k)$ and $P_{\delta \theta }(k)$. While this breaks down in the strongly non-linear regime, deviations can be modelled in terms of differences in the suppression factor, $g(a) = D(a)/a$, similar to those for the density field. Such modelling describes the differences in $P_{\theta \theta }(k)$ between models with the same linear clustering amplitude to better than 1 per cent accuracy at all scales and redshifts considered. Evolution–mapping simplifies the description of the cosmological dependence of non-linear density and velocity statistics, streamlining the sampling of large cosmological parameter spaces for cosmological analysis.