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The pairwise velocity probability density function in models with local primordial non-Gaussianity

We study how primordial non-Gaussianity affects the pairwise velocity probability density function (PDF) using an analytical model and cosmological N-body simulations. We adopt the local type non-Gaussian models characterized by f_{nl}, and examine both the linear velocity difference PDF and the linear pairwise velocity PDF. We show explicitly how f_{nl} induces correlations between originally independent velocities along the parallel and the perpendicular to the line of separation directions. We compare the model results with measurements from N-body simulations of the non-Gaussian models. Linear theory fails to predict the PDF in the f_{nl} models. Therefore we develop an analytic model based on the Zeldovich approximation to describe the evolution of the velocity PDF. Our analytical model and simulation results show remarkably good agreement in both the parallel and the perpendicular directions for the PDF profiles, as well as the change in the PDF due to primordial non-Gaussianity. The agreement is particularly good for relatively small separations (< 10 h^{-1} Mpc). The inclusion of the evolution of the velocity PDF is important to obtain a good description on the signature of primordial non-Gaussianity in the PDF. Our model provides the foundation to constrain f_{nl} using the peculiar velocity in future surveys.