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

TL;DR

This paper extends the evolution mapping approach to describe non-linear cosmic velocity field statistics, demonstrating its accuracy across different cosmologies and simplifying the analysis of cosmological parameters.

Contribution

It introduces an extension of evolution mapping to velocity statistics, validated with N-body simulations, enhancing the efficiency of cosmological parameter space sampling.

Findings

Evolution mapping accurately describes velocity divergence power spectra.

Deviations at small scales relate to differences in the suppression factor g(a).

The method simplifies the analysis of non-linear velocity and density statistics.

Abstract

We extend the evolution mapping approach, originally proposed by Sanchez (2022) 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, $P_L(k, z)$, and evolution parameters, which control its amplitude at any given redshift. Evolution mapping leverages the fact that density fluctuations in cosmologies with identical shape parameters but different evolution parameters exhibit remarkably similar non-linear evolutions when expressed as a function of the clustering amplitude. We use a suite of N-body simulations sharing identical shape parameters but spanning a wide range of evolution parameters. Using an efficient method for estimating the volume-weighted velocity field based on the Voronoi tesselation of the simulation particles, we study the non-linear evolution of the power spectra of the velocity divergence, $P_{\theta\theta}(k)$, and its cross-power spectrum with the density field, $P_{\delta\theta}(k)$. By analysing snapshots at redshifts where the linear matter perturbations have the same amplitude, we demonstrate that evolution mapping accurately applies to $P_{\theta\theta}(k)$ and $P_{\delta\theta}(k)$. Deviations at small scales can be modelled in terms of differences in the suppression factor, $g(a) = D(a)/a$, akin to those observed for the density field. 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 the analysis of cosmological observables.