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, $⟨0|0^{\prime }⟩$, between the unperturbed de Sitter vacuum $|0⟩$, and the state $|0^{\prime }⟩$ 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 $⟨0|0^{\prime }⟩\to 0$, 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.

22 pages + appendices, 3 figures. V2: Typos fixed, references and clarifications added