A non-polynomial gravity formulation for Loop Quantum Cosmology bounce

TL;DR

This paper introduces a non-polynomial gravity method to derive loop quantum cosmology-like bounce solutions, adding higher derivative terms to Einstein's action that produce second order equations in cosmological models.

Contribution

It proposes a novel non-polynomial gravity framework that reproduces loop quantum cosmology bounce features through higher derivative modifications.

Findings

Derived a new exact bounce solution in the modified gravity model.

Extended the model to include non-zero cosmological constant.

Demonstrated the second order nature of the resulting equations.

Abstract

Recently the so-called mimetic gravity approach has been used to obtain corrections to Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via the so-called non-polynomial gravity approach, which consists in adding geometric non-polynomial higher derivative terms to Hilbert-Einstein action, which are nonetheless polynomials and lead to second order differential equation in Friedmann-Lema\^itre-Robertson-Walker spacetimes. Our explicit action turns out to be a realization of the Helling proposal of effective action with infinite number of terms. The model is investigated also in presence of non vanishing cosmological constant and a new exact bounce solution is found and studied.