Unitarity of quantum-gravitational corrections to primordial fluctuations in the Born-Oppenheimer approach

We revisit the calculation of quantum-gravitational corrections to the power spectra of scalar and tensor perturbations in the Born-Oppenheimer approach to quantum gravity. We focus on the issue of the definition of the inner product of the theory and the unitarity of the corrections to the dynamics of the cosmological perturbations. We argue that the correction terms are unitary, provided the inner product is defined in a suitable way, which can be related to a notion of gauge fixing the time variable and the use of conditional probabilities in quantum cosmology. We compare the corrections obtained within this framework to earlier results in the literature and we conclude with some remarks on the physical interpretation of the correction terms.

Automated summary

This study revisits the calculation of quantum-gravitational corrections to the power spectra of scalar and tensor perturbations in the Born-Oppenheimer approach to quantum gravity. The focus is on defining the inner product of the theory and ensuring the unitarity of the corrections to the dynamics of the cosmological perturbations. The results suggest that the correction terms are unitary when the inner product is appropriately defined, which can be related to a notion of gauge fixing the time variable and using conditional probabilities in quantum cosmology.