Novel approach to the study of quantum effects in the early universe

TL;DR

This paper introduces a new theoretical framework for analyzing classical and quantum gravitational waves in the early universe using a nonlinear differential equation and Bogolubov transformations, with applications to de Sitter models.

Contribution

It develops a novel theoretical approach based on an auxiliary differential equation and quantum transformations to study gravitational waves in cosmology.

Findings

Derived an exact phase expression for gravitational waves.

Estimated quantum coherence destruction during cosmic evolution.

Applied the framework to quasi-de Sitter and de Sitter scenarios.

Abstract

We develop a theoretical frame for the study of classical and quantum gravitational waves based on the properties of a nonlinear ordinary differential equation for a function $\sigma(\eta)$ of the conformal time $\eta$, called the auxiliary field equation. At the classical level, $\sigma(\eta)$ can be expressed by means of two independent solutions of the ''master equation'' to which the perturbed Einstein equations for the gravitational waves can be reduced. At the quantum level, all the significant physical quantities can be formulated using Bogolubov transformations and the operator quadratic Hamiltonian corresponding to the classical version of a damped parametrically excited oscillator where the varying mass is replaced by the square cosmological scale factor $a^{2}(\eta)$. A quantum approach to the generation of gravitational waves is proposed on the grounds of the previous $\eta-$dependent Hamiltonian. An estimate in terms of $\sigma(\eta)$ and $a(\eta)$ of the destruction of quantum coherence due to the gravitational evolution and an exact expression for the phase of a gravitational wave corresponding to any value of $\eta$ are also obtained. We conclude by discussing a few applications to quasi-de Sitter and standard de Sitter scenarios.