Topology induced first-order phase transitions in lattice quantum gravity

Causal Dynamical Triangulations (CDT) is a lattice formulation of quantum gravity, suitable for Monte-Carlo simulations which have been used to study the phase diagram model. It has four phases characterized by different dominant geometries, denoted $A$, $B$, $C$ and $C_b$. In this article we analyse $A-B$ $B-C$ {phase} transitions in case where topology space that three-torus. This completes CDT such spatial topology. We observe order transition spacetime geometries can depend on spacetime.