Gaussianity of cosmic velocity fields and linearity of the velocity-gravity relation

We present a numerical study of the relation between the cosmic peculiar velocity field and the gravitational acceleration field. We show that on mildly non-linear scales (4-10 h^-1 Mpc Gaussian smoothing), the distribution of the Cartesian coordinates of each of these fields is well approximated by a Gaussian. In particular, their kurtoses and negentropies are small compared to those of the velocity divergence and density fields. We find that at these scales the relation between the velocity and gravity field follows linear theory to good accuracy. Specifically, the systematic errors in velocity-velocity comparisons due to assuming the linear model do not exceed 6 per cent in β. To correct for them, we test various non-linear estimators of velocity from density. We show that a slight modification of the α-formula proposed by Kudlicki et al. yields an estimator which is essentially unbiased and has a small variance.