The coincidence problem in $f(R)$ gravity models

TL;DR

This paper investigates how specific $f(R)$ gravity models in Einstein conformal frame can be designed to address the coincidence problem by choosing functions based on the deceleration parameter.

Contribution

It demonstrates that the $f(R)$ function can be tailored through the deceleration parameter to potentially resolve the coincidence problem in modified gravity models.

Findings

Certain $f(R)$ functions can avoid the coincidence problem

The approach links $f(R)$ form to deceleration parameter behavior

Models show potential for explaining dark energy dynamics

Abstract

To explore possibilities of avoiding coincidence problem in $f(R)$ gravity we consider models in Einstein conformal frame which are equivalent to Einstein gravity with a minimally coupled scalar field. As the conformal factor determines the coupling term and hence the interaction between matter and dark energy, the function $f(R)$ can in principle be determined by choosing an appropriate function for the deceleration parameter only. Possible behavior of $f(R)$ to avoid coincidence problem are investigated in two such cases.