Asymptotic symmetries in de Sitter and inflationary spacetimes

• Published in: Journal of cosmology and astroparticle physics Vol. 2017; no. 4; p. 33
• Main Authors: Ferreira, Ricardo Z., Sandora, McCullen, Sloth, Martin S.
• Format: Journal Article
• Language: English
• Published: United States 19.04.2017
• Subjects: ANISOTROPY; ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASYMPTOTIC SOLUTIONS; BREAKDOWN; COMPARATIVE EVALUATIONS; D S MESONS; DE SITTER SPACE; EXPANSION; GOLDSTONE BOSONS; GRAVITONS; INFLATIONARY UNIVERSE; SEMICLASSICAL APPROXIMATION; SPACE-TIME; SYMMETRY BREAKING
• ISSN: 1475-7516; 1475-7516
• DOI: 10.1088/1475-7516/2017/04/033

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'), 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 {sub p} {sup 2}/ H {sup 2} this overlap receives order one corrections and 0(0| 0')→ , which corresponds to an infrared perturbative breakdown after a time t {sub dS} ∼ M {sub p} {sup 2}/ H {sup 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.