Evaluating cosmic expansion \(f(\mathcal{T})\) vs \(f(R,T)\) gravity theories

Abstract

This study presents a comparative analysis of two modified theories of gravity, \(f(R,T)\) and \(f(\mathcal{T})\), within the framework of a locally rotationally symmetric Bianchi type-I spacetime. The primary objective is to explore the role of curvature-matter coupling and torsional dynamics in explaining the universe’s late-time acceleration without invoking a cosmological constant. To solve the highly nonlinear field equations, a hyperbolic sine scale factor and a shear-expansion proportionality condition are employed. The resulting models are constrained using observational Hubble parameter data via a \(\chi ^{2}\) minimization technique. Key cosmological quantities, including energy density, pressure, and the equation of state (EoS) parameter, are analyzed alongside geometrical diagnostics such as the \(\operatorname{Om}(z)\) and statefinder parameters. Statistical tools like the Akaike and Bayesian information criteria (AIC/BIC) are used to assess model performance relative to \(\Lambda\)CDM. Results show that both models capture the transition from decelerated to accelerated expansion, with the \(f(\mathcal{T})\) model exhibiting a more dynamic dark energy behavior and an earlier onset of acceleration. These findings suggest that torsional-based gravity may provide a geometrically motivated and observationally consistent alternative to standard cosmology.