A New Angle on Gravitational Clustering

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Abstract
A new approach to gravitational instability in large‐scale structure is described, 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 nonlinear 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 nonlinear perturbation theory in the transition to the nonlinear regime. We also consider the role of vorticity creation due to shell‐crossing and show using N‐body simulations for which at small (virialized) scales the velocity field reaches equipartition, that is, the vorticity power spectrum is about twice the divergence power spectrum.
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