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

Steven Weinberg

doi:10.1103/PhysRevD.79.043504

paper

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

arXiv:0810.2831 · doi:10.1103/PhysRevD.79.043504

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 $g_{ij} (x, t) / a^{2} (t)$ becomes a time-independent function $G_{ij} (x)$ , and all perturbations to the other metric components and to all matter variables vanish. The corrections are of order $a^{- 2}$ , and their $x$ -dependence is now explicitly given in terms of $G_{ij} (x)$ and its derivatives. The previous results for the time-dependence of the corrections to $g_{ij} (x, t) / a^{2} (t)$ 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.

15 pages

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

Abstract

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