Timelike boundaries in de Sitter JT gravity and the Gao-Wald theorem

TL;DR

This paper investigates how timelike boundaries in two-dimensional de Sitter JT gravity influence spacetime dynamics, revealing quantum effects that can cause the universe to become 'fatter' or 'taller' depending on boundary conditions.

Contribution

It analyzes quantum corrections from conformal matter in de Sitter JT gravity with different boundary types, showing how these affect spacetime geometry and energy conditions.

Findings

Vacuum stress tensor violates null energy condition with certain boundaries.

Quantum backreaction can increase the spacetime's size or height.

Different boundary conditions lead to distinct geometric responses.

Abstract

The Gao-Wald theorem says that de Sitter spacetime reacts to a positive energy perturbation by getting "taller." How does this change in the presence of timelike boundaries? We study this question in two-dimensional de Sitter JT gravity coupled to conformal matter. The effect of the boundaries has its roots in quantum corrections to the vacuum energy of the CFT due to Casimir-like effects. We consider two different kinds of timelike boundaries, either at locations where the coordinate $\varphi$ is constant or at locations where the dilaton is constant. For each kind we compute the vacuum expectation value of the matter CFT stress tensor. The stress tensor violates the null energy condition in the first case and saturates it in the second case, with each case exhibiting a negative energy density in the vacuum state. We then compute the semiclassical backreaction of this energy density and show how it can make the spacetime "fatter" or "taller" or a combination of both, depending on the regime. The spacetime getting fatter corresponds to an increase in the value of the dilaton at the horizon and hence also in the static patch horizon area in the higher-dimensional solution. We comment on the implications of our results for the quantum theories living on the timelike boundaries.