Matter-driven phase transition in lattice quantum gravity

The model of Causal Dynamical Triangulations (CDT) is a background-independent and diffeomorphism-invariant approach to quantum gravity,

which provides a lattice regularization of the formal gravitational path integral. The framework does not involve any coordinate system and employs only geometric invariants. For a Universe with toroidal spatial topology, we can introduce coordinates using classical scalar fields with periodic boundary conditions with a jump. The field configurations reveal pictures of cosmic voids and filaments surprisingly similar to the ones observed in the present-day Universe. I will discuss the impact of dynamical matter fields on the geometry of a typical quantum universe in the four-dimensional CDT model and explain several observed phenomena. In particular, a phase transition is triggered by the change of the scalar field jump amplitude. This discovery may have important consequences for quantum universes with non-trivial topology since the phase transition can change the topology to a simply connected one.