Effective actions for loop quantum cosmology in fourth-order gravity

Marcello Miranda; Daniele Vernieri; Salvatore Capozziello; Francisco S. N. Lobo

doi:10.1140/epjc/s10052-021-09767-5

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2021) 81: 975
https://doi.org/10.1140/epjc/s10052-021-09767-5

Regular Article - Theoretical Physics

Effective actions for loop quantum cosmology in fourth-order gravity

Marcello Miranda¹^,2^a, Daniele Vernieri²^,3, Salvatore Capozziello¹^,2^,3^,4 and Francisco S. N. Lobo⁵^,6

¹ Scuola Superiore Meridionale, Largo San Marcellino 10, 80138, Naples, Italy
² INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, 80126, Naples, Italy
³ Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”, Naples, Italy
⁴ Laboratory of Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050, Tomsk, Russia
⁵ Instituto de Astrofísica e Ciências do Espaco, Faculdade de Ciências da Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016, Lisbon, Portugal
⁶ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016, Lisbon, Portugal

^a marcello.miranda@unina.it

Received: 31 August 2021
Accepted: 21 October 2021
Published online: 6 November 2021

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 $R = g^{μ ν} R_{μ ν}$ $R=g^{\mu \nu }R_{\mu \nu }$ is the Ricci scalar, $P = R_{μ ν} R^{μ ν}$ $P=R_{\mu \nu }R^{\mu \nu }$ , and $Q = R_{α β μ ν} R^{α β μ ν}$ $Q=R_{\alpha \beta \mu \nu }R^{\alpha \beta \mu \nu }$ 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.

© The Author(s) 2021

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