Spectral geometry as a probe of quantum spacetime

TL;DR

This paper uses spectral geometry to analyze three-dimensional causal dynamical triangulations, providing evidence that the classical limit resembles de Sitter spacetime and confirming the phenomenon of dynamical dimensional reduction.

Contribution

It demonstrates that spectral geometry can identify the classical limit as de Sitter space and confirms dimensional reduction in 3D causal dynamical triangulations, a novel application.

Findings

Ground state resembles de Sitter spacetime

Confirmed dynamical dimensional reduction to spectral dimension ~2

First such confirmation in 3D causal dynamical triangulations

Abstract

Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of three-dimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the expectation value of the spectral dimension on the ensemble of geometries defined by these models, and comparing its large scale behaviour to that of a sphere (Euclidean de Sitter). From the same measurement we are also able to confirm the phenomenon of dynamical dimensional reduction observed in this and other approaches to quantum gravity -- the first time this has been done for three-dimensional causal dynamical triangulations. In this case, the value for the short-scale limit of the spectral dimension that we find is approximately 2. We comment on the relevance of these results for the comparison to asymptotic safety and Horava-Lifshitz gravity, among other approaches to quantum gravity.