Asymptotic Symmetries in de Sitter and Inflationary Spacetimes

Understand

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.