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

Abstract: 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 delta(4)(L), compared to delta(2)(L) of the linear velocity correlation function, and have the opposite sign. We present these terms up to delta(4)(L) 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 f sigma(8), using N-body simulations. We find that for a next-generation PV survey of volume similar to O(500 h(-1) Mpc)(3), these effects amount to a shift of f sigma(8) by similar to 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.

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