Pairwise Velocities as a Cosmological Probe

The mean pairwise velocity is a powerful cosmological probe, complementary to density-based statistics. On large scales it traces the background expansion; on small scales it is sensitive to non-linear structure formation. Working with the total matter distribution avoids tracer bias complications entirely. Pairwise velocities are also linked to observations through the kSZ effect, though current analyses are restricted to separations above ~20 Mpc/h. We quantify the cosmological constraining power gained by pushing into the non-linear regime, down to ~4 Mpc/h. Pairwise motions provide independent and complementary constraints on cosmological parameters, enhancing our understanding of structure formation and gravitational dynamics on small scales.