Dark Energy Behavior from Static Equation of State in Non-Minimally Coupled Gravity with Scalar Deformation

In this study, we explore the cosmological implications of a modified gravity theory characterized by the function $f(R, \Sigma, T)$, where $R$ is the Ricci scalar, $\Sigma$ represents a geometric deformation term, and $T$ denotes the trace of the energy-momentum tensor. The model is reconstructed under the framework of three fundamental energy conditions: Null Energy Condition (NEC), Dominant Energy Condition (DEC), and Strong Energy Condition (SEC). We derive the corresponding Hubble parameter $H(z)$ for each case and constrain the free parameters $H_0$, $\alpha$, and $\beta$ using the latest Cosmic Chronometer (CC) and Pantheon+ Type Ia Supernova datasets. A thorough analysis of physical quantities such as pressure, energy density, and the equation of state parameter is carried out. Furthermore, diagnostic tools including the deceleration parameter $q(z)$, statefinder parameters $\{r, s\}$, and the $O_m(z)$ diagnostic are employed to assess the models viability. Our findings suggest that the model can consistently describe late-time cosmic acceleration and offers distinct behavior under different energy conditions, all while aligning with current observational data.