Hubble parameter analysis of f(R,Σ,T) gravity: Confronting theory with recent data

The accelerating expansion of the universe has motivated the exploration of alternative gravity theories beyond General Relativity (GR). In this study, we investigate the cosmological implications of [Formula: see text] gravity, an extension of [Formula: see text] gravity that incorporates additional torsional scalar [Formula: see text], within a homogeneous and isotropic Friedmann–Robertson–Walker (FRW) metric. We derive the field equations and analyze the cosmic expansion, energy density, isotropic pressure, and equation of state parameter. To ensure observational consistency, we constrain the model parameters using Hubble parameter [Formula: see text] measurements and the Pantheon+ Type Ia supernovae dataset through a Markov Chain Monte Carlo (MCMC) analysis. Our findings indicate that this model naturally explains cosmic acceleration without requiring a cosmological constant, with results closely aligning with Planck data. The study further examines the energy conditions and the stability. The violation of the strong energy condition at late times supports the observed acceleration, consistent with other modified gravity frameworks. This work highlights the potential of [Formula: see text] gravity in explaining dark energy phenomena and motivates further theoretical and observational investigations.