In general terms my research focus is on field theoretical systems and topics related to quantum gravity. The systems include and resemble the velocity dominated limit of Einstein gravity, deemed to describe the vicinity of the Big Bang singularity. The velocity dominated theory has no dynamical spatial gradients and comes with its own Carroll geometry. Classical Einstein gravity can be mapped into this velocity dominated limit by means of a trivializing map, which systematically removes dynamical spatial gradients. A long term goal is to develop a quantum version of the ensued anti-Newtonian expansion. This includes two key issues absent on a classical level: first, an understanding of the interplay between asymptotic safety (UV complete renormalization group trajectories) and asymptotic velocity domination (backpropagation to the Big Bang dominated by velocity terms). Second, a proliferation of vacua seems to occur, so a characterization of their structure and signatures is needed. Often these problems can be concisely addressed in suitable model-systems, such as noncompact nonlinear sigma-models, quantum fields on Bianchi I backgrounds, quantum Gowdy cosmologies, and others.