QUASI-LINEAR EVOLUTION OF COMPENSATED COSMOLOGICAL PERTURBATIONS - THE NONLINEAR-SIGMA-MODEL

We consider the evolution of perturbations to a flat FRW universe that arise from a ''stiff source,'' such as a self-ordering cosmic field t hat forms in a global symmetry-breaking phase transition and evolves v ia the Kibble mechanism. Although the linear response of the normal ma tter to the source depends on the details of the source dynamics, we s how that the higher-order nonlinear perturbative equations reduce to a form identical to those of source-free Newtonian gravity in the small wavelength limit. Consequently, the resulting n-point correlation fun ctions and their spectral counterparts will have a hierarchical contri bution arising from this gravitational evolution (as in the source-fre e case) in addition to that possibly coming from non-Gaussian initial conditions. We apply this formalism to the O(N) nonlinear sigma model at large N and find that observable differences from the case of initi ally Gaussian perturbations and Newtonian gravity in the bispectrum an d higher-order correlations are not expected on scales smaller than ab out 100h-1 Mpc.