Isometric evolution in de Sitter quantum gravity

TL;DR

This paper investigates time evolution in de Sitter quantum gravity models, revealing isometric rather than unitary evolution and proposing a matrix model dual for Jackiw-Teitelboim gravity with a varying boundary dilaton.

Contribution

It demonstrates that de Sitter quantum gravity exhibits isometric evolution and introduces a matrix model dual with a boundary dilaton variation.

Findings

Time evolution in de Sitter models is isometric, not unitary.

States leading to crunches are projected out during evolution.

A matrix model dual for Jackiw-Teitelboim gravity is established.

Abstract

We study time evolution in two simple models of de Sitter quantum gravity, Jackiw-Teitelboim gravity and a minisuperspace approximation to Einstein gravity with a positive cosmological constant. In the former we find that time evolution is isometric rather than unitary, and find suggestions that this is true in Einstein gravity as well. The states that are projected out under time evolution are initial conditions that crunch. Along the way we establish a matrix model dual for Jackiw-Teitelboim gravity where the dilaton varies on the boundary.