We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly atâ€¦ (More)

Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. Weâ€¦ (More)

We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, theâ€¦ (More)

Fruitful ideas on how to quantize gravity are few and far between. In this paper, we give a complete description of a recently introduced non-perturbative gravitational path integral whose continuumâ€¦ (More)

We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized non-perturbative state sum over simplicial Lorentzian spacetimes, each possessing a unique Wickâ€¦ (More)

The volume operator is an important kinematical quantity in the non-perturbative approach to four-dimensional quantum gravity in the connection formulation. We give a general algorithm for computingâ€¦ (More)

We uncover a surprising correspondence between a non-perturbative formulation of three-dimensional Lorentzian quantum gravity and a hermitian two-matrix model with ABAB-interaction. The gravitationalâ€¦ (More)

It is well-known that the sum over topologies in quantum gravity is ill-defined, due to a super-exponential growth of the number of geometries as a function of the space-time volume, leading to aâ€¦ (More)

We construct explicitly a (12g âˆ’ 12)-dimensional space P of unconstrained and independent initial data for â€™t Hooftâ€™s polygon model of (2+1) gravity for vacuum spacetimes with compact genus-gâ€¦ (More)

The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantumâ€¦ (More)