Two dimensional Nearly de Sitter gravity

Abstract

We study some aspects of the de Sitter version of Jackiw-Teitelboim gravity. Though we do not have propagating gravitons, we have a boundary mode when we compute observables with a fixed dilaton and metric at the boundary. We compute the no-boundary wavefunctions and probability measures to all orders in perturbation theory. We also discuss contributions from different topologies, borrowing recent results by Saad, Shenker and Stanford. We discuss how the boundary mode leads to gravitational corrections to cosmological observables when we add matter. Finally, starting from a four dimensional gravity theory with a positive cosmological constant, we consider a nearly extremal black hole and argue that some observables are dominated by the two dimensional nearly de Sitter gravity dynamics.

66 pp, 15 figs; v4: Appendix added on the identification between the wave function obtained from the path integral and the Wheeler de Witt equation