Characteristics of the new phase in CDT

The approach of Causal Dynamical Triangulations (CDT), a candidate theory of nonperturbative quantum gravity in 4D, turns out to have a rich phase structure. We investigate the recently discovered bifurcation phase \(C_{b}\) and relate some of its characteristics to the presence of singular vertices of very high order. The transition lines separating this phase from the “time-collapsed” B-phase and the de Sitter phase \(C_{dS}\) are of great interest when searching for physical scaling limits. The work presented here sheds light on the mechanisms behind these transitions. First, we study how the B–\(C_{b}\) transition signal depends on the volume fixing implemented in the simulations, and find results compatible with the previously determined second-order character of the transition. The transition persists in a transfer matrix formulation, where the system’s time extension is taken to be minimal. Second, we relate the new \(C_{b}\)–\(C_{dS}\) transition to the appearance of singular vertices, which leads to a direct physical interpretation in terms of a breaking of the homogeneity and isotropy observed in the de Sitter phase when crossing from \(C_{dS}\) to the bifurcation phase \(C_{b}\).