Does f(R,T) gravity admit a stationary scenario between dark energy and dark matter in its framework?

Abstract

In this note we address the well-known cosmic coincidence problem in the framework of the \textit{f(R,T)} gravity. In order to achieve this, an interaction between dark energy and dark matter is considered. A constraint equation is obtained which filters the \textit{f(R,T)} models that produce a stationary scenario between dark energy and dark matter. Due to the absence of a universally accepted interaction term introduced by a fundamental theory, the study is conducted over three different forms of chosen interaction terms. As an illustration three widely known models of \textit{f(R,T)} gravity are taken into consideration and used in the setup designed to study the problem. The study reveals that, the realization of the coincidence scenario is almost impossible for the popular models of $f(R,T)$ gravity, thus proving to be a major setback for these models.