The bounce universe history from unimodular $F(R)$ gravity

TL;DR

This paper explores how various cosmological bouncing models can be realized within unimodular $F(R)$ gravity, analyzing their perturbations, stability, and implications for the cosmological constant problem.

Contribution

It demonstrates the realization of multiple bouncing cosmologies in unimodular $F(R)$ gravity and examines their stability, perturbations, and potential to address the cosmological constant problem.

Findings

Different bouncing models have distinct perturbation behaviors.

Unimodular $F(R)$ gravity does not modify Newton's law.

The theory is ghost-free and stable against matter perturbations.

Abstract

In this paper we investigate how to realize various quite well known cosmological bouncing models in the context of the recently developed unimodular $F(R)$ gravity. Particularly, we shall study the matter bounce scenario, the singular bounce, the superbounce and a symmetric bounce scenario. We present the behavior of the Hubble radius for each of the bouncing models we shall take into account and we investigate which era of the bouncing model is responsible for the cosmological perturbations. As we shall demonstrate, the various bouncing models do not behave in the same way, so the cosmological perturbations for each model may correspond to a different era, in comparison to other models. Also we present which unimodular $F(R)$ gravity realizes each model. We also show that Newton's law is not modified in the unimodular $F(R)$ gravity, which also is proven to be a ghost-free theory, and in addition we discuss the matter stability issue. Finally, we demonstrate how it is possible to solve a cosmological constant problem in the context of unimodular $F(R)$ gravity.