Nonlinear effects on cosmological perturbations. I - The evolution of adiabatic perturbations. II - The production of isothermal perturbations by a primordial sound spectrum
The nonlinear evolution of a power spectrum of adiabatic perturbations in the early universe is calculated under the assumptions of random phase and weak nonlinearity. Results agree with previous results of an ideal nonrelativistic gas, and are an extension of Peeble's formula. Nonlinear dissipation dominates the evolution of the power spectrum at all frequencies where the total linear dissipation has decreased the initial amplitude by more than one e-fold, which increases the amount of power at high frequencies where the linear theory predicts an exponential decrease. In addition, computer simulations of the evolution of reasonable adiabatic perturbation spectra are presented.