Density matrix of de Sitter JT gravity

TL;DR

This paper investigates the quantum properties of de Sitter JT gravity, revealing a mixed ground state and analyzing wave functions and probability distributions related to the universe's size.

Contribution

It provides an exact analysis of the density matrix and wave functions in de Sitter JT gravity, highlighting the mixed nature of the ground state and connections to complex geometries.

Findings

Ground state is a mixed state, not pure.

Results align with semiclassical double-trumpet amplitudes.

Probability distribution for universe size is flat.

Abstract

Jackiw-Teitelboim (JT) gravity in two-dimensional de Sitter space is an intriguing toy model for a quantum mechanical description of an inflationary phase of the universe, including initial conditions. Starting from exact solutions of the Wheeler-DeWitt equation, we study a conditional density matrix of the system. We find that the ground state is a mixed state, rather than a pure Hartle-Hawking state. Our results are consistent with the semiclassical double-trumpet amplitude, and with recent work on complex geometries containing bra-ket wormholes. We also analyze semiclassical wave functions for metric, dilaton, and an additional inflaton field. The probability distribution for the size of the universe is flat.