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

Understand

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 $g_{ij}({\bf x},t)/a^2(t)$ becomes a time-independent function ${\cal G}_{ij}({\bf x})$, and all perturbations to the other metric components and to all matter variables vanish.
• The corrections are of order $a^{-2}$, and their ${\bf x}$-dependence is now explicitly given in terms of ${\cal G}_{ij}({\bf x})$ and its derivatives.
• The previous results for the time-dependence of the corrections to $g_{ij}({\bf x},t)/a^2(t)$ in the case of multi-scalar field theories are now shown to apply for any theory whose anisotropic inertia vanishes to order $a^{-2}$.