Quantum Cosmology and the Evolution of Inflationary Spectra

TL;DR

This paper develops a method to calculate quantum gravitational effects on primordial inflationary spectra using the Wheeler-De Witt approach, analyzing different inflationary models and comparing results with observations.

Contribution

It introduces a canonical quantization framework with quantum-gravitational corrections for inflationary spectra analysis, applying a Born-Oppenheimer approach to the matter-gravity system.

Findings

Quantum-gravitational corrections to spectra derived

Analytical results compared with observational data

Parameter estimation using Monte Carlo Markov Chain

Abstract

We illustrate how it is possible to calculate the quantum gravitational effects on the spectra of primordial scalar/tensor perturbations starting from the canonical, Wheeler-De Witt, approach to quantum cosmology. The composite matter-gravity system is analysed through a Born-Oppenheimer approach in which gravitation is associated with the heavy degrees of freedom and matter (here represented by a scalar field) with the light ones. Once the independent degrees of freedom are identified the system is canonically quantised. The differential equation governing the dynamics of the primordial spectra with its quantum-gravitational corrections is then obtained and is applied to diverse inflationary evolutions. Finally, the analytical results are compared to observations through a Monte Carlo Markov Chain technique and an estimate of the free parameters of our approach is finally presented and the results obtained are compared with previous ones.