Quantization of perturbations during inflation in the 1+3 covariant formalism

TL;DR

This paper develops a covariant formalism for quantizing scalar and tensor perturbations during inflation, extending the Mukhanov-Sasaki variables within the 1+3 covariant approach and discussing generalizations to non-flat universes.

Contribution

It introduces a covariant framework for perturbation quantization during inflation, generalizing Mukhanov-Sasaki variables to the 1+3 formalism and non-flat universes.

Findings

Derived covariant Mukhanov-Sasaki variables for scalar and tensor perturbations

Discussed extension to non-flat Friedmann-Lemaitre universes

Provided a foundation for covariant perturbation analysis during inflation

Abstract

This note derives the analogue of the Mukhanov-Sasaki variables both for scalar and tensor perturbations in the 1+3 covariant formalism. The possibility of generalizing them to non-flat Friedmann-Lemaitre universes is discussed.