Dynamics of Solutions of $f(R)$ Theory

TL;DR

This paper investigates the late-time behavior of solutions in $f(R)$ gravity theories by leveraging their correspondence with Einstein-scalar field systems, demonstrating conditions for accelerated cosmic expansion.

Contribution

It establishes a link between $f(R)$ functions and scalar field potentials, deriving new conditions for accelerated expansion in $f(R)$ gravity models.

Findings

Proves accelerated expansion for specific classes of $f(R)$ functions.

Identifies restrictions on $f(R)$ based on scalar field potential assumptions.

Utilizes known scalar field results to analyze $f(R)$ solutions.

Abstract

We use the correspondence between the $f(R)$ theory and an Einstein-scalar field system to study late-time dynamics of solutions of $f(R)$ theory. We discuss how reasonable assumptions on the potential of the scalar field lead to restrictions on the function $f(R)$ and use known results for the scalar field system to gain results on solutions of the $f(R)$ theory. In particular, we prove accelerated expansion at late times for several different categories of functions $f(R)$ that satisfy certain restrictions.