Gauge-invariant perturbations at a quantum gravity bounce

TL;DR

This paper investigates gauge-invariant scalar perturbations in quantum gravity bounce cosmologies, revealing conditions under which key perturbation variables are conserved or not across the bounce.

Contribution

It extends the understanding of perturbation conservation laws to a broader class of modified Friedmann equations in quantum gravity scenarios.

Findings

$$ is conserved across the bounce in certain models.

$$ and $al R$ are equal on super-horizon scales for adiabatic perturbations.

Conservation of perturbations depends on the specific form of the modified Friedmann equations.

Abstract

We study the dynamics of gauge-invariant scalar perturbations in cosmological scenarios with a modified Friedmann equation, such as quantum gravity bouncing cosmologies. We work within a separate universe approximation which captures wavelengths larger than the cosmological horizon; this approximation has been successfully applied to loop quantum cosmology and group field theory. We consider two variables commonly used to characterise scalar perturbations: the curvature perturbation on uniform-density hypersurfaces $\zeta$ and the comoving curvature perturbation $\mathcal{R}$. For standard cosmological models in general relativity as well as in loop quantum cosmology, these quantities are conserved and equal on super-horizon scales for adiabatic perturbations. Here we show that while these statements can be extended to a more general form of modified Friedmann equations similar to that of loop quantum cosmology, in other cases, such as the simplest group field theory bounce scenario, $\zeta$ is conserved across the bounce whereas $\mathcal{R}$ is not. We relate our results to approaches based on a second order equation for a single perturbation variable, such as the Mukhanov-Sasaki equation.