A FROZEN-FLOW APPROXIMATION TO THE EVOLUTION OF LARGE-SCALE STRUCTURES IN THE UNIVERSE

A new approximation to the evolution of large-scale structures in the Universe is proposed which is based on neglecting the role of particle inertia compared to the damping implied by the Hubble drag. We call this approximation frozen flow because particles move by updating at each step their velocity to the local value of the peculiar velocity field, here approximated by its growing linear mode: stream-lines are then frozen to their initial shape. The situation is quite different from that of the Zel'dovich algorithm, where the velocity is kept constant along each particle trajectory. The advantage of this approximation is that the emerging density field is free of singularities: no caustics appear at finite time. This property allows an extrapolation into the non-linear regime beyond the time at which shell crossings would have appeared according to the Zel'dovich approximation. We test the validity of this method by applying it to suitable toy models and by following the evolution of large-scale structures, starting from the standard cold dark matter initial power spectrum of Gaussian perturbations. A formal connection between this approximation and the adhesion model is pointed out.