On the Problem of Time in Asymptotically Safe Quantum Gravity

Quantum gravity has often been approached by scholars, as well as presented to the general public, as a very special theoretical subject, which needs a peculiar treatment, starting with the resolution of its foundational issues. Among the latter, the problem of time, also called the problem of reparametrization invariance, has often been particularly highlighted. Other notable and related challenges are the question of emergence or fundamentality of spacetime, and the construction of a space of states, of a probability interpretation, of a complete cosmological evolution. Nonetheless, a particular line of research called asymptotically safe quantum gravity still tries to make sense of the topic by quantizing general relativity on the same footing as any other field theory. Despite apparently ignoring or avoiding a direct confrontation with the above-mentioned foundational problems, this formulation of quantum gravity leads to a definite view on them. This contribution provides a brief introduction to the asymptotic safety scenario for quantum gravity, especially focusing on the role that the problem of time and its related foundational questions have within this formulation. We review the recent developments and proposals towards some of the ultimate quantum-gravity research goals: background invariance, unitarity, cosmology and the origin of scales.