Asymptotic Symmetries in de Sitter and Inflationary Spacetimes

TL;DR

This paper explores the role of asymptotic symmetries and soft gravitons in de Sitter and inflationary spacetimes, revealing their physical effects, charge constructions, and implications for vacuum stability and perturbative breakdown.

Contribution

It explicitly constructs charges associated with asymptotic symmetries in de Sitter space and analyzes their physical effects, extending the understanding to inflationary scenarios.

Findings

Soft gravitons act as Nambu-Goldstone bosons of broken asymptotic symmetries.

Vacuum overlaps decay to zero after a certain timescale, indicating perturbative breakdown.

Re-derivation of inflationary consistency relations and their relation to asymptotic symmetries.

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.