The time-dependent mass of cosmological perturbations in loop quantum cosmology: Dapor-Liegener regularization

TL;DR

This paper calculates the time-dependent masses for scalar and tensor perturbations in loop quantum cosmology using Dapor-Liegener regularization, comparing two main formalisms and analyzing their positivity during key cosmological phases.

Contribution

It introduces a detailed computation of perturbation masses within Dapor-Liegener regularization and compares hybrid and dressed metric formalisms in this context.

Findings

Masses are computed for both formalisms.

Positivity of masses is analyzed during the big bounce.

Comparison reveals differences between the two approaches.

Abstract

In this work, we compute the time-dependent masses that govern the dynamics of scalar and tensor perturbations propagating on an effective flat, homogeneous, and isotropic background within the framework of loop quantum cosmology, regularized according to the procedure put forward by Dapor and Liegener. To do so, we follow the two main approaches that, in the field of loop quantum cosmology, lead to hyperbolic equations for the perturbations in the ultraviolet sector: the hybrid and dressed metric formalisms. This allows us to compare the masses resulting from both proposals and analyze their positivity in regimes of physical interest: the big bounce and the contracting de Sitter phase in the asymptotic past that is a defining feature of the model under consideration.