Matter Bounce Loop Quantum Cosmology from $F(R)$ Gravity

TL;DR

This paper explores which $F(R)$ gravity theories can produce matter bounce scenarios consistent with Loop Quantum Cosmology, analyzing early and late cosmic times, and comparing inflation predictions with Planck data.

Contribution

It identifies specific $F(R)$ models compatible with matter bounce scenarios in Loop Quantum Cosmology, including their inflationary behavior and observational consistency.

Findings

Late-time $F(R)$ reduces to Einstein-Hilbert plus power law

Explicit scalar field solutions for early-time high curvature

Inflationary predictions align with Planck data after holonomy corrections

Abstract

Using the reconstruction method, we investigate which $F(R)$ theories, with or without the presence of matter fluids, can produce the matter bounce scenario of holonomy corrected Loop Quantum Cosmology. We focus our study in two limits of the cosmic time, the large cosmic time limit and the small cosmic time limit. For the former, we found that, in the presence of non-interacting and non-relativistic matter, the $F(R)$ gravity that reproduces the late time limit of the matter bounce solution is actually the Einstein-Hilbert gravity plus a power law term. In the early time limit, since it corresponds to large spacetime curvatures, assuming that the Jordan frame is described by a general metric that when it is conformally transformed to the Einstein frame, produces an accelerating Friedmann-Robertson-Walker metric, we found explicitly the scalar field dependence on time. After demonstrating that the solution in the Einstein frame is indeed accelerating, we calculate the spectral index derived from the Einstein frame scalar-tensor counterpart theory of the $F(R)$ theory and compare it with the Planck experiment data. In order to implement the resulting picture, we embed the $F(R)$ gravity explicitly in a Loop Quantum Cosmology framework by introducing holonomy corrections to the $F(R)$ gravity. In this way, the resulting inflation picture corresponding to the $F(R)$ gravity can be corrected in order it coincides to some extent with the current experimental data.