Dynamics of pairwise motions in the fully non-linear regime in LCDM and Modified Gravity cosmologies

In contrast to our understanding of density field tracers, the modelling of direct statistics pertaining to the cosmic velocity field remains open to significant opportunities for improvement. The lack of accurate modelling for the non-linear domain of pairwise velocities restricts our capacity to fully exploit the information encoded in this observable. We present a robust approach for modelling the mean infall velocities, $v_{12}(r,a)$, with broad applicability spanning sub-megaparsec scales and cosmologies extending beyond the standard LCDM paradigm. Our approach involves solving the full pair-conservation equation using accurate non-linear power spectrum descriptions. To assess the robustness of our model, we extend it to cosmologies beyond the standard LCDM, in particular, the Hu-Sawicki $f(R)$-gravity and Dvali-Gabadadze-Porrati (DGP) modified gravity models. Remarkably, our predictions for pairwise velocities of dark matter particles at kilo-parsec scales exhibit excellent agreement with N-body simulations throughout the entire dynamical range ($0.1 \lesssim \xi \lesssim 1000$, or $r\geq0.4$Mpc/h). Furthermore, we show that different gravity models leave distinct signatures in the shape and dynamics of the mean pairwise velocities, providing a potent test of cosmological gravity laws.