Euclidean volume fluctuations in de Sitter quantum gravity

TL;DR

This paper investigates the probability distribution of the volume in de Sitter quantum gravity using Euclidean methods, revealing how quantum effects influence the likelihood of different universe sizes.

Contribution

It derives volume probability distributions in de Sitter quantum gravity across multiple approximation levels, including exact 2D results, highlighting quantum effects on universe size.

Findings

Distribution concentrates around classical volume in the classical limit.

Quantum effects cause the distribution to spread and favor smaller universes.

Results are consistent across various approximation methods.

Abstract

The Euclidean formulation of quantum gravity can be interpreted in terms of a probability distribution over Riemannian manifolds. In the context of de Sitter gravity, the statistics of the total volume according to this distribution is encoded in the dependence of the partition function on the cosmological constant. We use this observation to obtain a probability distribution for the volume from known results and proposals for the de Sitter partition function, in several levels of approximation: saddle point, one loop, an all-loop and a non-perturbative proposal in 3 dimensions, and an exact result in 2 dimensions, in the context of Liouville theory. In all cases we find a reasonable behavior: in the classical limit the distribution concentrates around the classical volume, and it spreads as quantum effects are turned on. We also find as a common trend that, as quantum effects are increased, the probability distribution favors increasingly smaller universes.