Analysis of the Semiclassical Solution of CDT

TL;DR

This paper analyzes Monte Carlo simulation data of 3+1 dimensional causal dynamical triangulations (CDT), confirming the existence of a semiclassical limit and exploring the form of the effective discrete action including all simplex types.

Contribution

It provides the first detailed analysis of the semiclassical limit in 3+1D CDT and investigates the form of the extended discrete action incorporating all simplex types.

Findings

Existence of a semiclassical limit for (4,1) simplices confirmed

Effective semiclassical solutions valid with all simplex types included

Form of the extended discrete action characterized

Abstract

Causal dynamical triangulations (CDT) constitute a background independent, nonperturbative approach to quantum gravity, in which the gravitational path integral is approximated by the weighted sum over causally well-behaving simplicial manifolds i.e. causal triangulations. This thesis is an analysis of the data from the Monte Carlo computer simulations of CDT in 3+1 dimensions. It is confirmed here that there exist the semiclassical limit of CDT for so-called (4,1) (or equivalent (1,4)) simplices, being a discrete version of the mini-superspace model. Next, the form of the corresponding discrete action is investigated. Furthermore, it is demonstrated that the effective, semiclassical solution works also after the inclusion of remaining (3,2) and (2,3) simplices, treated collectively. A specific form of the resulting extended discrete action is examined and a transition from the broader framework to the former narrower one is shown.