The Causal Dynamical Triangulations (CDT) model is a background-independent and diffeomorphism-invariant approach to quantum gravity that provides a lattice regularization of the formal gravitational path integral. The framework does not require a coordinate system, but uses only geometric invariants. We introduce coordinates via scalar fields with a target space whose topology matches the topology of spacetime. I will present the impact of dynamical matter fields on the geometry of a typical quantum universe in the four-dimensional CDT model. In particular, I will discuss a phase transition induced by matter fields.