Cosmological implications of f ( R , Σ , T ) gravity using the Efstathiou equation of state in FLRW spacetime

Abstract We explore the cosmological behavior of the recently proposed f ( R , Σ , T ) gravity theory, which generalizes the standard f ( R , T ) framework by incorporating an additional Ricci-torsion scalar Σ to account for torsion-induced effects within the spacetime geometry. Employing the Efstathiou equation of state (EoS) parameterization in a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) background, we derive the modified field equations and analytically reconstruct the Hubble parameter. The model parameters are constrained using the Cosmic Chronometer ( CC ) and Pantheon+SH0ES supernova datasets through Markov Chain Monte Carlo analysis. Our results reveal that the f ( R , Σ , T ) framework can successfully reproduce the late-time accelerated expansion of the Universe without the need for an explicit cosmological constant. The resulting effective EoS evolves within the quintessence regime and approaches the ΛCDM limit at low redshift. Furthermore, energy conditions, sound speed stability, and thermodynamic consistency are examined, confirming the physical viability of the model. These findings suggest that the inclusion of the Ricci-torsion term Σ offers a promising geometrical mechanism for cosmic acceleration and helps alleviate current observational tensions in Hubble parameter measurements.