Quantum gravity Vs unimodular quantum gravity

Strong gravity tests indicate that general relativity is a very accurate description of the classical dynamics of spacetime even at extreme regimes. Yet, the same dynamics can be described by "alternative" versions of general relativity such as unimodular gravity. In the quest for a quantum theory of the gravitational field, it is unclear if the quantization of such classically equivalent theories leads to the same physical predictions. In this talk, I will report on some recent results regarding this issue in the framework of continuum and perturbative quantum field theory. With a view towards ultraviolet completion, I will discuss some evidence for asymptotic safety in unimodular quantum gravity. Moreover, I will comment on the role of matter fields which couple very differently to gravity in those settings.