Evolution mapping II: describing statistics of the non-linear cosmic velocity field.

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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, PL(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 tesselation of simulation particles, we study the non-linear evolution of the velocity divergence power spectrum, Pθθ(k), and its cross-power spectrum with the density field, Pδθ(k). We demonstrate that the evolution mapping relation applies accurately to Pθθ(k) and Pδθ(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 Pθθ(k) between models with the same linear clustering amplitude to better than 1percnt 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.