Coincidence Problem in $f(R)$ Gravity Models

TL;DR

This paper investigates how $f(R)$ gravity models, equivalent to Einstein gravity with a scalar field, can address the coincidence problem by analyzing the scalar field's coupling to matter.

Contribution

It derives a necessary condition for alleviating the coincidence problem within $f(R)$ gravity models formulated in the Einstein conformal frame.

Findings

Derived a condition for alleviating the coincidence problem

Linked $f(R)$ models to scalar field interactions with matter

Provided theoretical insights into modified gravity's cosmological implications

Abstract

The $f(R)$ gravity models formulated in Einstein conformal frame are equivalent to Einstein gravity together with a minimally coupled scalar field. The scalar field couples with the matter sector and the coupling term is given by the conformal factor. We use this interacting model to derive a necessary condition for alleviating the coincidence problem.