Asymptotic Symmetries in de Sitter and Inflationary Spacetimes

Abstract

Soft gravitons produced by the expansion of de Sitter can be viewed as the Nambu-Goldstone bosons of spontaneously broken asymptotic symmetries of the de Sitter spacetime. We explicitly construct the associated charges, and show that acting with the charges on the vacuum creates a new state equivalent to a change in the local coordinates induced by the soft graviton. While the effect remains unobservable within the domain of a single observer where the symmetry is unbroken, this change is physical when comparing different asymptotic observers, or between a transformed and un-transformed initial state, consistent with the scale-dependent statistical anisotropies previously derived using semiclassical relations. We then compute the overlap, $\langle0| 0'\rangle$, between the unperturbed de Sitter vacuum $|0\rangle$, and the state $| 0'\rangle$ obtained by acting $\mathcal{N}$ times with the charge. We show that when $\mathcal{N}\to M_p^2/H^2$ this overlap receives order one corrections and $\langle0| 0'\rangle\to 0$, which corresponds to an infrared perturbative breakdown after a time $t_{dS} \sim M_p^2/H^3$ has elapsed, consistent with earlier arguments in the literature arguing for a perturbative breakdown on this timescale. We also discuss the generalization to inflation, and rederive the 3-point and one-loop consistency relations.