Energy Conditions in Higher Derivative $f(R,\Box R,T)$ Gravity

In this paper, we examined the viability bounds of a higher derivative $f(R,\Box R, T)$ theory through analyzing energy conditions (where $R$ and $T$ are the Ricci scalar and trace of energy momentum tensor, respectively). We take flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetime coupled with ideal configurations of matter content. We consider three different realistic models of this gravity, that could be utilized to understand the stability of cosmological solutions. After constructing certain bounds mediated by energy conditions, more specifically weak energy condition, we discuss viable zones of the under considered modified models in an environment of recent estimated numerical choices of the cosmic parameters.