The cosmological perturbation theory in loop cosmology with holonomy corrections

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.

18 pages,typos corrected, reference added, version published in JCAP

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• Non-Gaussian features from the inverse volume corrections in loop quantum cosmology
• Anomaly freedom of the vector modes with holonomy corrections in perturbative Euclidean loop quantum gravity
• Dynamics of k-essence in loop quantum cosmology
• Power spectrum and anisotropy of super inflation in loop quantum cosmology