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 \( f(R, Σ, T) \), where \( R \) is the Ricci scalar, \( Σ\) 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 \( H_0 \), \( α\), and \( β\) 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.