Parameter sensitivity of cosmic pairwise velocities in the non-linear regime of structure formation

The peculiar velocities of dark matter tracers drive the growth of cosmic structures, providing a sensitive test of cosmological models and strengthening constraints on the nature of dark energy. In this work, we investigate the mean pairwise velocities, $v_{12}$, of dark matter tracers as a cosmological probe in the non-linear regime of cosmic structure formation. Using N-body dark matter-only simulations, we measure $v_{12}$ for pair separations up to 50 $h^{-1}$Mpc and model it by solving the pair conservation equation for a self-gravitating particle system, along with various prescriptions of the nonlinear matter power spectrum. We quantified the sensitivity of $v_{12}$ to variations in key cosmological parameters such as $\Omega_{\mathrm{m}}$, $\sigma_8$, $h$, $M_\nu$, and $w$. Our parameter inference analysis using MCMC shows sub-11% agreement with simulation data, with notable degeneracies, particularly between $\Omega_\mathrm{m}$ and $\sigma_8$. We further compute the stable clustering crossing scale across redshifts $z=0$, $0.5$, and $1$, assessing its dependence on cosmology. Among the tested power spectrum modeling approaches, we find that the CSSTEmu emulator provides the most accurate predictions, with deviations below 5% for $r > 10$ $h^{-1}$Mpc at $z=0.5$. Our results are validated using independent simulation suites, demonstrating that our framework offers a robust method for extracting cosmological constraints from upcoming peculiar velocity data.