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.

http://arxiv.org/icons/sfx.gif

Comments are closed, but trackbacks and pingbacks are open.