DeWitt wave functions for de Sitter JT gravity

TL;DR

This paper studies wave functions in de Sitter JT gravity, finding solutions that vanish at singular boundaries, supporting DeWitt's conjecture, and explores the limitations of semiclassical approximations.

Contribution

It provides a systematic analysis of Wheeler-DeWitt solutions with Schwarzian asymptotics in de Sitter JT gravity, confirming DeWitt's boundary condition and discussing superpositions to avoid singularities.

Findings

Real analytic solutions vanish at the boundary, supporting DeWitt's conjecture.

Superpositions of solutions can avoid singularities in expanding and contracting branches.

The analysis highlights limitations of semiclassical wave functions in this context.

Abstract

Jackiw-Teitelboim (JT) gravity in two-dimensional de Sitter space is an intriguing model for cosmological "wave functions of the universe". Its minisuperspace version already contains all physical information. The size of compact slices is parametrized by a scale factor $h > 0$. The dilaton $\phi$ is chosen to have positive values, $\phi > 0$, and interpreted as size of an additional compact slice in a higher-dimensional theory. At the boundaries $h=0$, $\phi=0$, where the volume of the universe vanishes, the curvature is generically singular. According to a conjecture by DeWitt, solutions of the Wheeler-DeWitt (WDW) equation should vanish at singular loci. Recently, the behaviour of JT wave functions at large field values $h$, $\phi$ has been obtained by means of a path integral over Schwarzian degrees of freedom of a boundary curve. We systematically analyze solutions of the WDW equation with Schwarzian asymptotic behaviour. We find real analytic solutions that vanish on the entire boundary, in agreement with DeWitt's conjecture. Projection to expanding and contracting branches may lead to singularities, which can however be avoided by an appropriate superposition of solutions. Our analysis also illustrates the limitations of semiclassical wave functions.