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[en] In this manuscript, we are interested to address the issue of cosmic expansion in the background of matter-geometry coupling. For this purpose we consider modified theory (where is the Ricci Scalar, is the trace of energy-momentum tensor (EMT) and is interaction of EMT and Ricci Tensor ). We formulate modified field equations in the background of flat Friedmann-Lemaître-Robertson-Walker (FLRW) model which is defined as , where represents the scale factor. In this formalism energy density is found using covariant divergence of modified field equations. involves a contribution from non-minimal matter geometry coupling which helps to study different cosmic eras based on equation of state (EOS). Furthermore, we apply the energy bounds to constrain the model parameters establishing a pathway to discuss the cosmic evolution for best suitable parameters in accordance with recent observations.