Covariant Effective Action for Loop Quantum Cosmology a la Palatini

TL;DR

This paper derives a covariant effective action for loop quantum cosmology, connecting the discrete quantum geometry with continuum descriptions and enabling the study of gauge-invariant cosmological perturbations.

Contribution

It introduces an algorithm to obtain a covariant effective action from loop quantum cosmology, establishing the theory's covariance and continuum properties.

Findings

Effective action derived for loop quantum cosmology.

Covariance of the quantum gravity effects established.

Potential for analyzing gauge-invariant cosmological perturbations.

Abstract

In loop quantum cosmology, non-perturbative quantum gravity effects lead to the resolution of the big bang singularity by a quantum bounce without introducing any new degrees of freedom. Though fundamentally discrete, the theory admits a continuum description in terms of an effective Hamiltonian. Here we provide an algorithm to obtain the corresponding effective action, establishing in this way the covariance of the theory for the first time. This result provides new insights on the continuum properties of the discrete structure of quantum geometry and opens new avenues to extract physical predictions such as those related to gauge invariant cosmological perturbations.