A New Angle on Gravitational Clustering

Abstract

We describe a new approach to gravitational instability in large-scale structure, where the equations of motion are written and solved as in field theory in terms of Feynman diagrams. The basic objects of interest are the propagator (which propagates solutions forward in time), the vertex (which describes non-linear interactions between waves) and a source with prescribed statistics which describes the effect of initial conditions. We show that loop corrections renormalize these quantities, and discuss applications of this formalism to a better understanding of gravitational instability and to improving non-linear perturbation theory in the transition to the non-linear regime. We also consider the role of vorticity creation due to shell-crossing and show using N-body simulations that at small (virialized) scales the velocity field reaches equipartition, i.e. the vorticity power spectrum is about twice the divergence power spectrum.