Cosmological perturbations in a class of fully covariant modified theories: Application to models with the same background as standard LQC

TL;DR

This paper develops a covariant modified gravity framework that reproduces the background dynamics of standard Loop Quantum Cosmology and derives perturbation equations, providing a new approach to quantum-corrected cosmological models.

Contribution

It introduces a covariant class of modified gravity theories that replicate LQC background evolution and derives perturbation equations consistent with LQC results.

Findings

Reproduces LQC background equations with a covariant modified gravity

Tensor perturbation equations match those of GR in this framework

Scalar perturbation equations resemble LQC deformed algebra approach

Abstract

Bouncing cosmologies are obtained by adding to the Einstein-Hilbert action a term of the form $\sqrt{-g}f(\chi)$, with $\chi$ a scalar depending on the Hubble parameter only, not on its derivatives, and which is here shown to arise from the divergence of the unitary time-like eigenvector of the stress tensor. At background level, the dynamical equations for a given $f$-theory are calculated, showing that the simplest bouncing cosmology resulting leads to exactly the same equations as those for holonomy corrected Loop Quantum Cosmology (LQC). When dealing with perturbations, the equation for tensor ones is the same as in General Relativity (GR); for scalar perturbations, when one uses the $f$-theory which leads to the same background as the standard version of holonomy corrected LQC, one obtains similar equations (although a bit more elaborated) as those coming from LQC in the so-called deformed algebra approach.