Non-Gaussian Correlations Outside the Horizon

Abstract

It is shown that under essentially all conditions, the non-linear classical equations governing gravitation and matter in cosmology have a solution in which far outside the horizon in a suitable gauge the reduced spatial metric (the spatial metric divided by the square of the Robertson--Walker scale factor $a$) is time-independent, though with an arbitrary dependence on co-moving coordinates, and all perturbations to the other metric components and to all matter variables vanish, to leading order in $1/a$. The corrections are of order $1/a^2$, and are explicitly given for the reduced metric in a multifield model with a general potential. Further, this is the solution that describes the metric and matter produced by single-field inflation. These results justify the use of observed non-Gaussian correlations (or their absence) as a test of theories of single-field inflation, despite our ignorance of the constituents of the universe while fluctuations are outside the horizon after inflation, as long as graphs with loops can be neglected.