Effective Actions for Loop Quantum Cosmology in Fourth-Order Gravity

Abstract

Loop Quantum Cosmology (LQC) is a theory which renders the Big Bang initial singularity into a quantum bounce, by means of short range repulsive quantum effects at the Planck scale. In this work, we are interested in reproducing the effective Friedmann equation of LQC, by considering a generic $f(R,P,Q)$ theory of gravity, where $R=g^{\mu \nu }{R}_{\mu \nu }$ is the Ricci scalar, $P=R_{\mu \nu }{R}^{\mu \nu }$, and $Q=R_{\alpha \beta \mu \nu }{R}^{\alpha \beta \mu \nu }$ is the Kretschmann scalar. An order reduction technique allows us to work in $f(R,P,Q)$ theories which are perturbatively close to General Relativity, and to deduce a modified Friedmann equation in the reduced theory. Requiring that the modified Friedmann equation mimics the effective Friedmann equation of LQC, we are able to derive several functional forms of $f(R,P,Q)$. We discuss the necessary conditions to obtain viable bouncing cosmologies for the proposed effective actions of $f(R,P,Q)$ theory of gravity.

arXiv commentv1: 15 pages; v2: 16 pages. Matches published version in EPJC

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Cited by in corpus (6)

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• Effective $f(R)$ actions for modified Loop Quantum Cosmologies via order reduction
• A diffeomorphism invariant family of metric-affine actions for loop cosmologies
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