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 nonlinear regime of cosmic structure formation. Using $N$-body dark matter-only simulations, we measure $v_{12}$ for pair separations up to $50h^{-1}\mathrm{Mpc}$ 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 ${\mathrm{\Omega }}_{\mathrm{m}}$, ${\sigma }_8$, $h$, $M_{\nu }$, and $w$. Our parameter inference analysis using Markov chain Monte Carlo (MCMC) shows sub-11% agreement with simulation data, with notable degeneracies, particularly between ${\mathrm{\Omega }}_m$ 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 $r>10h^{-1}\mathrm{Mpc}$ 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.

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• Cosmological parameters
• Dark energy
• Large scale structure of the Universe