Effective Actions for Loop Quantum Cosmology in Fourth-Order Gravity. (arXiv:2107.07777v2 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Miranda_M/0/1/0/all/0/1">Marcello Miranda</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Vernieri_D/0/1/0/all/0/1">Daniele Vernieri</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Capozziello_S/0/1/0/all/0/1">Salvatore Capozziello</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Lobo_F/0/1/0/all/0/1">Francisco S. N. Lobo</a>

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 $R=g^{munu}R_{munu}$ is the Ricci scalar,
$P=R_{munu}R^{munu}$, and $Q=R_{alphabetamunu}R^{alphabetamunu}$ 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.

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 $R=g^{munu}R_{munu}$ is the Ricci scalar,
$P=R_{munu}R^{munu}$, and $Q=R_{alphabetamunu}R^{alphabetamunu}$ 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.

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