Transitioning from a bounce to $R^2$ inflation

TL;DR

This paper presents a classical bouncing cosmology model with an $R^2$ term in modified gravity, which naturally transitions into an inflationary phase, addressing early universe singularities and stability issues.

Contribution

It introduces a novel bouncing model incorporating $R^2$ gravity that smoothly transitions into inflation, improving upon previous models by analyzing stability with the scalaron.

Findings

The universe undergoes a bounce followed by inflation driven by $R^2$ term.

The scalaron enhances the stability of the bouncing inflationary model.

The model aligns with observational data on early universe dynamics.

Abstract

Non-singular bouncing cosmologies are well--motivated models for the early universe. Recent observational data are consistent with positive spatial curvature and allow for a natural collapsing and bouncing phase in the very early universe. Additionally, bouncing cosmologies have the potential to rectify conceptual shortcomings identified in the theory of inflation, such as the singularity problem. In this paper we present a classical bouncing model in the context of modified gravity, including an $R^2$-term in the action. We show that after the bounce, the universe enters naturally a period of inflation, driven by the $R^2$--term. We analyse the stability of the model and find that the scalaron assists the stability of the model.