Impact of topology in causal dynamical triangulations quantum gravity

Understand

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.