Quantum Cosmology and the Inflationary Spectra from a Non-Minimally Coupled Inflaton

TL;DR

This paper derives quantum gravitational corrections to inflationary perturbations in non-minimally coupled inflaton models using a Born-Oppenheimer approach, extending previous minimal coupling analyses and addressing the problem of time in quantum cosmology.

Contribution

It generalizes the quantum correction framework for inflationary spectra to non-minimal coupling cases, including induced gravity, and introduces a new method for handling the time problem.

Findings

Quantum gravitational corrections are derived for non-minimally coupled inflaton models.

The approach is extended to include induced gravity scenarios.

A generalized method for the time problem in quantum cosmology is proposed.

Abstract

We calculate the quantum gravitational corrections to the Mukhanov-Sasaki equation obtained by the canonical quantization of the inflaton-gravity system. Our approach, which is based on the Born-Oppenheimer decomposition of the resulting Wheeler-DeWitt equation, was previously applied to a minimally coupled inflaton. In this article we examine the case of a non minimally coupled inflaton and, in particular, the induced gravity case is also discussed. Finally, the equation governing the quantum evolution of the inflationary perturbations is derived on a de Sitter background. Moreover the problem of the introduction of time is addressed and a generalized method, with respect to that used for the minimal coupling case, is illustrated. Such a generalized method can be applied to the universe wave function when, through the Born-Oppenheimer factorization, we decompose it into a part which contains the minisuperspace degrees of freedom and another which describes the perturbations.