LAUSR

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 f(R,T,Q)$f(R,T,Q)$ modified theory (where R$R$ is the Ricci Scalar, T$T$ is the trace of energy-momentum tensor (EMT) Tuv$T_{uv}$ and Q=RuvTuv$Q=R_{uv}T^{uv}$ is interaction of EMT Tμν$T_{\mu \nu }$ and Ricci Tensor Ruv$R_{uv}$). We formulate modified field equations in the background of flat Friedmann-Lemaître-Robertson-Walker (FLRW) model which is defined as ds2=dt2−a(t)2(dx2+dy2+dz2)$ds^{2}=dt^{2}-a(t)^{2}(dx^{2}+dy^{2}+dz^{2} )$, where a(t)$a(t)$ represents the scale factor. In this formalism energy density is found using covariant divergence of modified field equations. ρ$\rho $ 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.