Asymptotic symmetries in de Sitter and inflationary spacetimes

Abstract

Soft gravitons produced by the expansion of de Sitter can be viewed as the NambuGoldstone 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 , between the unperturbed de Sitter vacuum |0 , and the state |0 obtained by acting N times with the charge. We show that when N → M 2 p /H 2 this overlap receives order one corrections and 0|0 → 0, which corresponds to an infrared perturbative breakdown after a time t dS ∼ M 2 p /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.

Search optimization, funnel topography, and dynamical criticality on the string landscape

“…Remarkably, this optimal lifetime coincides with the dS Page time [104]. The dS Page time has appeared in other inflationary studies before [105][106][107][108]. In slow-roll inflation, for instance, it marks the phase transition to eternal inflation [109,110].…”

“…Remarkably, this is recognized as the Page time [104] for dS space [105][106][107][108]. In slow-roll inflation, the Page time marks the phase transition to slow-roll eternal inflation [109] and has been used to place a bound on the maximum number of e-folds that can be described semi-classically [110].…”

Electromagnetic duality and the electric memory effect

“…the absence of light-like null infinity or the existence of a horizon makes closure of the triangular relation more challenging. Yet, some of these IR relations seem to hold even in cosmological backgrounds [10][11][12][13][14][15] where the spacetime is not asymptotically flat. On the other hand, the conceptual and technical difficulties arising from the close connection between the background spacetime and the LGTs do not exist in Abelian gauge theory like quantum electrodynamics (QED) in flat spacetime [16,17].…”

Large gauge transformation, soft theorem, and Infrared divergence in inflationary spacetime

“…This ensures the absence of the IRdiv due to the soft graviton in the correlation functions of g R evaluated for | Ψ . By contrast, when we evaluate a correlation function for an operator which does not preserve the genuine gauge invariance, the insertion of the soft graviton changes the correlation function and this can lead to a break down of the perturbative expansion [71,73]. (See also ref.…”