The cosmological perturbation theory in loop cosmology with holonomy corrections

TL;DR

This paper explores how holonomy corrections in loop quantum cosmology affect scalar metric perturbations in a flat FRW universe, revealing new contributions to the perturbation equations.

Contribution

It derives the cosmological perturbation equations incorporating holonomy corrections within the Hamiltonian framework, highlighting their influence on both background and perturbations.

Findings

Holonomy corrections introduce non-trivial terms in perturbation equations.

Both background and perturbation dynamics are affected by holonomy effects.

New terms $S_{h1}$ and $S_{h2}$ appear in the equations.

Abstract

In this paper we investigate the scalar mode of first-order metric perturbations over spatially flat FRW spacetime when the holonomy correction is taken into account in the semi-classical framework of loop quantum cosmology. By means of the Hamiltonian derivation, the cosmological perturbation equations is obtained in longitudinal gauge. It turns out that in the presence of metric perturbation the holonomy effects influence both background and perturbations, and contribute the non-trivial terms $S_{h1}$ and $S_{h2}$ in the cosmological perturbation equations.