Nonlinear velocity power spectrum: modeling the cosmological dependence on the Hubble constant and cold dark matter density

In this paper we present a semi-analytical model for the velocity power spectrum in $\text{La}$CDM cosmology for wave numbers $k<1\mathrm{/}$Mpc. We mainly concentrate on the dominant divergence part but also present some results on the vorticity contribution. We divide cosmological parameters into evolution and shape parameters and model the dependence of the evolution parameter $h$ and of the shape parameter ${\text{om}}_{\mathrm{c}\mathrm{d}\mathrm{m}}$ with an accuracy better than 2.5%. A surprising finding of our study is that the velocity power spectrum becomes independent of ${\text{om}}_{\mathrm{c}\mathrm{d}\mathrm{m}}$ on nonlinear scales. A python implementation of the model is publicly available.