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

TL;DR

This paper investigates the unitarity of quantum-gravitational corrections to primordial fluctuations within the Born-Oppenheimer approach, emphasizing the importance of inner product definition and gauge choices for consistent quantum cosmology predictions.

Contribution

It clarifies how to define the inner product to ensure unitarity of quantum-gravitational corrections in the Born-Oppenheimer framework for cosmological perturbations.

Findings

Quantum-gravitational correction terms are unitary with proper inner product definition.

Comparison with previous results shows consistency when gauge-fixing is appropriately applied.

Remarks on the physical interpretation of correction terms highlight their significance in quantum cosmology.

Abstract

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.