The results of a recent paper [Phys. Rev. D 78, 123521 (2008)] are generalized. A more detailed proof is presented that under essentially all conditions, the nonlinear 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 $g_{ij}(\mathbf{x},t)/a^2(t)$ becomes a time-independent function ${\mathcal{G}}_{ij}(\mathbf{x})$, and all perturbations to the other metric components and to all matter variables vanish. The corrections are of order $a^{-2}$, and their $\mathbf{x}$ dependence is now explicitly given in terms of ${\mathcal{G}}_{ij}(\mathbf{x})$ and its derivatives. The previous results for the time dependence of the corrections to $g_{ij}(\mathbf{x},t)/a^2(t)$ in the case of multiscalar 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 nonzero conserved quantities, and the $O(a^{-2})$ corrections to the other dynamical variables are explicitly calculated in both cases.

• Received 29 November 2008

DOI:https://doi.org/10.1103/PhysRevD.79.043504