Perturbed quantum gravity bounces: Approaching inhomogeneity in group field theory

In this thesis we investigate cosmological perturbations around a quantum gravity bounce from a model-agnostic perspective as well as from the viewpoint of group field theory. Bounces provide a resolution to the Big Bang singularity and can be found in theories of quantum gravity, such as group field theory and loop quantum cosmology. They manifest in an effective Friedmann equation that is calculated directly from the quantum theory and encodes quantum corrections to high curvature regimes. Going beyond the dynamics of the homogeneous background spacetime to include also cosmological perturbations in a framework of quantum gravity is often a highly non-trivial task.

We investigate to what extent the separate universe framework can be used to extract information about the dynamics of gauge-invariant perturbations on super-horizon scales around a quantum gravity bounce. We find that for modified Friedmann equations similar to that of loop quantum cosmology, the conservation laws of general relativity continue to apply. More generally, however, these perturbations can become dynamical, as is the case in e.g. group field theory.

Independent from the cosmological setting, we make a more general proposal to reconstruct an effective metric from group field theory. Our proposition relies on symmetries that exist both in the classical as well as in the quantum framework. We promote the resulting Noether currents of the quantum theory to operators and identify their expectation values with their classical counterparts. Applying this procedure to the cosmological setting allows us to reconstruct expressions for effective metric perturbations from group field theory directly and opens up the possibility to investigate gauge-invariant quantities. While we can extract a flat Friedmann-Lemaître-Robertson-Walker metric at late times, the effective perturbations we recover for our choice of quantum state do no exhibit the dynamics of general relativity in the semiclassical regime.