Impact of topology in causal dynamical triangulations quantum gravity

TL;DR

This study explores how changing the spatial topology in 3+1 dimensional causal dynamical triangulations affects quantum gravity, revealing that topology influences the effective action and the resulting classical background geometry.

Contribution

It demonstrates that spatial topology alters the effective potential in CDT, allowing for a constant average volume distribution and identifying classical backgrounds without predefined geometries.

Findings

Toroidal topology yields a constant average volume distribution.

The effective potential changes with topology, affecting quantum fluctuations.

Classical background geometries are identifiable in the quantum theory.

Abstract

We investigate the impact of spatial topology in 3+1 dimensional causal dynamical triangulations (CDT) by performing numerical simulations with toroidal spatial topology instead of the previously used spherical topology. In the case of spherical spatial topology we observed in the so-called phase C an average spatial volume distribution n(t) which after a suitable time redefinition could be identified as the spatial volume distribution of the four-sphere. Imposing toroidal spatial topology we find that the average spatial volume distribution n(t) is constant. By measuring the covariance matrix of spatial volume fluctuations we determine the form of the effective action. The difference compared to the spherical case is that the effective potential has changed such that it allows a constant average n(t). This is what we observe and this is what one would expect from a minisuperspace GR action where only the scale factor is kept as dynamical variable. Although no background geometry is put in by hand, the full quantum theory of CDT is also with toroidal spatial toplogy able to identify a classical background geometry around which there are well defined quantum fluctuations.