Non-Gaussian Correlations Outside the Horizon II: The General Case

The results of a recent paper [0808.2909] are generalized. A more detailed proof is presented that under essentially all conditions, the non-linear classical equations governing matter and gravitation in cosmology have “adiabatic” solutions in which, far outside the horizon, in a suitable gauge, the reduced spatial metric gij(x, t)/a 2(t) becomes a time-independent function Gij(x), and all perturbations to the other metric components and to all matter variables vanish. The corrections are of order a−2, and their xdependence is now explicitly given in terms of Gij(x) and its derivatives. The previous results for the time-dependence of the corrections to gij(x, t)/a 2(t) in the case of multi-scalar field theories are now shown to apply for any theory whose anisotropic inertia vanishes to order a−2. Further, it is shown that the adiabatic solutions are attractive as a becomes large for the case of single field inflation and now also for thermal equilibrium with no non-zero conserved quantities, and the O(a−2) corrections to the other dynamical variables are explicitly calculated in both cases. ∗Electronic address: [email protected]