Impact of topology in causal dynamical triangulations quantum gravity

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.

22 pages, 10 figures

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Cited by in corpus (22)

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• Towards reconstructing the quantum effective action of gravity
• Functional Renormalization Group flows on Friedman-Lema\^ıtre-Robertson-Walker backgrounds
• The phase structure of Causal Dynamical Triangulations with toroidal spatial topology
• Four-dimensional CDT with toroidal topology
• On the scaling of composite operators in Asymptotic Safety
• Towards an UV fixed point in CDT gravity
• CDT and Cosmology
• Critical Phenomena in Causal Dynamical Triangulations
• Cosmic voids and filaments from quantum gravity
• Pseudo-Cartesian coordinates in a model of Causal Dynamical Triangulations
• Matter-driven change of spacetime topology
• Scalar fields in Causal Dynamical Triangulations
• Generalised spectral dimensions in non-perturbative quantum gravity
• Topology induced first-order phase transitions in lattice quantum gravity
• The phase structure and effective action of 3D CDT at higher spatial genus
• Scales and hierachies in asymptotically safe quantum gravity: a review
• Yang--Mills topology on four-dimensional triangulations
• CDT Quantum Toroidal Spacetimes: An Overview
• Minisuperspace results for causal dynamical triangulations