I aim to connect various non-perturbative approaches to quantum gravity, which often involve some form of discrete structures, to more conventional physical theories based on general relativity. At the moment I am focussing on the derivation of classical cosmology from fundamental quantum gravity, and various models of quantum cosmology.
The most natural place to look for testable predictions from quantum gravity is in cosmology. A major first step towards making the connection to cosmology is to be able to describe quantum gravity states that describe macroscopic, homogeneous or approximately homogeneous universes like the one around us, and to be able to do calculations within quantum gravity to derive the effective dynamics of such states. With Daniele Oriti and Lorenzo Sindoni, I have recently managed to complete these steps in the group field theory approach to quantum gravity. We show that certain states whose structure is analogous to condensate states that appear in Bose-Einstein condensation describe macroscopic spatially homogeneous geometries, and that in a semiclassical regime and in the isotropic case, the dynamics they satisfy is given precisely by the Friedmann equation for pure GR.
These results have started a whole new programme for connecting effective quantum cosmology models with fundamental theories of quantum gravity, which I keep exploring with Daniele Oriti and others. For instance, I currently investigate extensions of the formalism to matter fields and inhomogeneities.