Quantum corrections to the Mukhanov-Sasaki equations

TL;DR

This paper develops new technical tools and a systematic procedure to analyze quantum corrections to the Mukhanov-Sasaki equations, aiming to improve predictions of primordial fluctuations in quantum cosmology.

Contribution

It introduces an interaction picture approach to handle quantum corrections beyond common approximations, enhancing analysis of quantum effects on cosmological perturbations.

Findings

New method to extract quantum dynamics of homogeneous geometry

Procedures to analyze interaction evolution in quantum corrections

Enhanced ability to discriminate between quantization proposals

Abstract

Recently, a lot of attention has been paid to the modifications of the power spectrum of primordial fluctuations caused by quantum cosmology effects. The origin of these modifications are corrections to the Mukhanov-Sasaki equations that govern the propagation of the primeval cosmological perturbations. The specific form of these corrections depends on a series of details of the quantization approach and of the prescription followed to implement it. Generally, nonetheless, the complexity of the theoretical quantum formulation is simplified in practice appealing to a semiclassical or effective approximation, in order to perform concrete numerical computations. In this work, we introduce technical tools and design a procedure to deal with these quantum corrections beyond the most direct approximations employed so far in the literature. In particular, by introducing an interaction picture, we extract the quantum dynamics of the homogeneous geometry in absence of scalar field potential and inhomogeneities, dynamics that has been intensively studied and that can be integrated. The rest of our analysis focuses on the interaction evolution, putting forward methods to cope with it. The ultimate aim is to develop treatments that increase our ability to discriminate between the predictions of different quantization proposals for cosmological perturbations.