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

TL;DR

This paper generalizes previous results on adiabatic solutions in cosmology, showing their stability and explicit correction terms outside the horizon for a broad class of theories, including inflation and thermal equilibrium scenarios.

Contribution

It extends the proof of adiabatic solutions outside the horizon to more general theories and explicitly calculates correction terms, demonstrating their attractiveness in various cosmological models.

Findings

Adiabatic solutions become time-independent outside the horizon.

Corrections are explicitly proportional to derivatives of ${f G}_{ij}({f x})$.

Adiabatic solutions are stable in single field inflation and thermal equilibrium.

Abstract

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 $a^{-2}$. 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.