Effective Theories of Redshift-Space Galaxy Peculiar Velocities

Abstract: We present predictions for redshift-space peculiar velocity statistics in the Lagrangian and Eulerian formulations of the effective field theory (EFT) of large-scale structure. We compute 2-point pairwise velocity statistics up to the second moment at next-to-leading (1-loop) order, showing that they can be modeled together with redshift-space galaxy densities with a consistent set of EFT coefficients. We show that peculiar velocity statistics have a distinct dependence on long-wavelength bulk flows that necessitates a variation on the usual infrared (IR) resummation procedure used to model baryon acoustic oscillations (BAO) in galaxy clustering. This can be implemented recursively in powers of the velocity in both the Lagrangian and Eulerian frameworks. We validate our analytic calculations against fully nonlinear N-body simulations, demonstrating that they can be used to recover the growth rate at better than percent level precision, well beyond the statistical requirements of upcoming peculiar velocity surveys and measurements of the kinetic Sunyaev-Zeldovich (kSZ) effect. As part of this work, we release $\texttt{velocisaurus}$, a fast $\texttt{Python}$ code for computing EFT predictions of peculiar velocity statistics.