2008/10/16 by Steven Weinberg · 1 citation
Physics and Astronomy · #hep-ph #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.79.043504
published as Phys.Rev.D79:043504,2009 · 15 pages
arxiv created 2008/10/16 · arxiv updated 2010/04/21
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(\bf x,t)/a2(t) becomes a time-independent function \cal Gij(\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 Gij(\bf x) and its derivatives. The previous results for the time-dependence of the corrections to gij(\bf x,t)/a2(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.