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

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 $Λ$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.