Non-linear Pairwise Velocities as a Cosmological Probe

Peculiar velocities trace gravitational dynamics directly, complementing density-based clustering as wide-field spectroscopic surveys (DESI, Euclid, PFS) and kinetic Sunyaev-Zel'dovich (kSZ) measurements enter the precision era. Observational analyses of pairwise velocities and the pairwise kSZ signal remain largely restricted to linear and quasi-linear scales (20-30 h-1Mpc), despite substantial cosmological information available at smaller separations. We present a simulation-calibrated likelihood for v 12(r,a), built on the exact pair conservation equation and PyCAMB HMcode-2020 non-linear clustering, and validate it against the QUIJOTE and TNG300-3 suites across resolution, particle sampling, box size, and redshift. Using QUIJOTE, we show that extending the fit to non-linear scales tightens the 1σ uncertainty on Ω m and σ 8 by 74% and 81% at z=0.5 (r min=4 h-1Mpc), and by 70% and 74% at z=0 (r min=8 h-1Mpc), relative to the linear-regime baseline (r min=50 h-1Mpc) (all at fixed r max=140 h-1Mpc); σ(fσ 8) tightens by up to 86%, and the joint Ω m - fσ 8 Figure-of-Merit improves by up to 9.1 times relative to the same baseline. These constraints are conditional on h fixed at its QUIJOTE fiducial value, due to a near-degenerate response with σ 8; jointly sampling h shifts and widens them substantially. This framework provides a validated route to exploiting that information in upcoming direct peculiar-velocity, redshift-space, and kSZ analyses.