The effects of non-linearity on the growth rate constraint from velocity correlation functions

The two-point statistics of the cosmic velocity field, measured from galaxy peculiar velocity (PV) surveys, can be used as a dynamical probe to constrain the growth rate of large-scale structures in the universe. Most works use the statistics on scales down to a few tens of Megaparsecs, while using a theoretical template based on the linear theory. In addition, while the cosmic velocity is volume-weighted, the observable line-of-sight velocity two-point correlation is density-weighted, as sampled by galaxies, and therefore the density-velocity correlation term also contributes, which has often been neglected. These effects are fourth order in powers of the linear density fluctuation δ_ L^4, compared to δ_ L^2 of the linear velocity correlation function, and have the opposite sign. We present these terms up to δ_ L^4 in real space based on the standard perturbation theory, and investigate the effect of non-linearity and the density-velocity contribution on the inferred growth rate fσ_8, using N-body simulations. We find that for a next-generation PV survey of volume ∼ O(500 h^-1 Mpc)^3, these effects amount to a shift of fσ_8 by ∼ 10 per cent and is comparable to the forecasted statistical error when the minimum scale used for parameter estimation is r_ min = 20 h^-1 Mpc.