Semiclassical and Continuum Limits of Four-Dimensional CDT

TL;DR

This paper explores the limits of four-dimensional Causal Dynamical Triangulations (CDT), demonstrating how it recovers classical gravity in certain phases and discussing the potential for a non-perturbative quantum gravity theory via continuum limits and renormalization group flow.

Contribution

It provides insights into the semiclassical and continuum limits of 4D CDT, including phase transition analysis and the prospects for a UV fixed point in quantum gravity.

Findings

Recovery of a four-dimensional semiclassical universe in the de Sitter phase

Fluctuations of the scale factor are well-described by a minisuperspace effective action

Higher-order phase transitions suggest the possibility of defining a continuum limit

Abstract

This article discusses the infrared and the (perspective) ultraviolet limits of four-dimensional Causal Dynamical Triangulations (CDT). CDT is a non-perturabtive and background-independent approach to quantization of Einstein's gravity, based on a lattice regularization of the quantum-gravitational path integral. It is shown that inside the, so-called, de Sitter phase one recovers a four-dimensional semiclassical universe, where behaviour of the scale factor is consistent with classical solutions of Einstein's field equations and fluctuations of the scale factor are very accurately described by a simple minisuperspace effective action. It is argued that some of the phase transitions bordering the semiclassical phase are higher-order transitions, which opens a possibility of defining a continuum limit of CDT. Finally, it is discussed how to define the renormalization group flow in CDT and then how to search for a UV fixed point in which, in the spirit of asymptotic safety, quantum theory of gravity could become non-perturbatively renormalizable and thus valid up to arbitrarily short distance scales.