Time in quantum cosmology

Understand

A cosmological model with two global internal times shows that time reparameterization invariance, and therefore covariance, is not guaranteed by deparameterization.

• In particular, it is impossible to derive proper-time effective equations from a single deparameterized model if quantum corrections from fluctuations and higher moments are included.
• The framework of effective constraints shows how proper-time evolution can consistently be defined in quantum cosmological systems, such that it is time reparameterization invariant when compared with other choices of coordinate time.
• At the same time, it allows transformations of moment corrections in different deparameterizations of the same model, indicating partial time reparameterization of internal-time evolution.