Improving the reconstruction of the velocity potential and primordial density fluctuations by choice of smoothing windows

Recently considerable attention has been focused on improving algorithms for restoring primordial density fluctuations in the universe or investigating large-scale velocity fields by going to higher order approximations relating nonlinear states to their initial conditions. An alternative approach is to investigate the use of alternative smoothing windows within the context of first-order approximations. I present evidence that the universally used Gaussian smoothing window is far from optimal. A sharp truncation P(k) = 0 for k greater than k(c) leads to a much more direct connection to initial conditions for either 'Gaussianization' methods or use of the Zel'dovich approximation, as discussed in the text.