Revisiting The Coincidence Problem in $f(R)$ Gravitation

TL;DR

This paper examines whether interacting dark matter and dark energy in $f(R)$ gravity models can solve the Coincidence Problem, finding that the solution is highly model-dependent and not universally applicable.

Contribution

It tests the effectiveness of a previously proposed interaction technique in $f(R)$ gravity models for addressing the Coincidence Problem, revealing its limited model independence.

Findings

Interaction technique is not universally effective across models.

Model dependence is significant in solving the Coincidence Problem.

Alternative model-independent approaches are needed.

Abstract

The energy densities of dark matter (DM) and dark energy (DE) are of the same order at the present epoch despite the fact that both these quantities have contrasting characteristics and are presumed to have evolved distinctively with cosmic evolution. This is a major issue in standard $\Lambda$CDM cosmology and is termed "The Coincidence Problem" which hitherto cannot be explained by any fundamental theory. In this spirit, Bisabr \cite{bisabr} reported a cosmological scenario in $f(R)$ gravity where DM and DE interact and exchange energy with each other and therefore evolve dependently. We investigate the efficiency and model independancy of the technique reported in Bisabr \cite{bisabr} in addressing the Coincidence problem with the help of two $f(R)$ gravity models with model parameters constrained from various observations. Our result confirm the idea that not all scalar-tensor gravity theories and models can circumvent the Coincidence Problem and any cosmological scenario with interacting fluids is highly model dependent and hence alternate model independent theories and ideas should be nominated to solve this mystery.