Effective actions for loop quantum cosmology in fourthorder gravity
Abstract
Loop quantum cosmology (LQC) is a theory which renders the Big Bang initial singularity into a quantum bounce, by means of shortrange 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^{μ ν}R_{μ ν} is the Ricci scalar, P =R_{μ ν}R^{μ ν} , and Q =R_{α β μ ν}R^{α β μ ν} 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.
 Publication:

European Physical Journal C
 Pub Date:
 November 2021
 DOI:
 10.1140/epjc/s10052021097675
 arXiv:
 arXiv:2107.07777
 Bibcode:
 2021EPJC...81..975M
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 v1: 15 pages