Impact of Torsion–Trace Coupling on Anisotropic Compact Stars Using the MIT Bag Model

Over the past decade, the accelerated expansion of the universe has remained a central topic of discussion, particularly in the contexts of the late-time cosmic acceleration (dark energy era), the rapid inflationary phase, and the radiation-dominated early epoch. Motivated by these phenomena, this study investigates the role of anisotropic compact stellar configurations within the framework of modified gravity. Specifically, we extend the conventional f ( T ) gravity to its generalized form f ( T, τ ) gravity, adopting the model f ( T , τ ) = α T ( r ) + β τ ( r ) + ϕ , where T denotes the torsion scalar, τ represents the trace of the energy–momentum tensor, ϕ is the cosmological constant, and α, β are arbitrary constants. Since spherically symmetric spacetimes closely approximate realistic stellar systems, we construct compact star models within this geometry. To determine the metric potentials, we employ the embedding class one approach, commonly referred to as the Karmarkar condition, which reduces the problem to a single differential equation linking the two metric functions. Assuming the radial component g rr , the temporal component g tt is subsequently obtained through this condition. The constants of the model are constrained by applying the Darmois–Israel junction conditions, ensuring a smooth matching between the interior and exterior spacetimes. For physical validation, we utilize observed mass and radius data of compact stars such as S A X J 1808.4 − 3658 , V e l a X − 1 , P S R J 1614 − 2230 , and P S R J 0952 − 0607 . A comprehensive analysis is then performed using the Tolman–Oppenheimer–Volkoff (TOV) equations, along with graphical examinations of the equation of state, mass-radius relation, causality conditions, sound speed profiles, redshift, and compactness. Our findings confirm that the proposed stellar configurations are stable, physically viable, and consistent with observational constraints, thereby supporting the applicability of f ( T, τ ) gravity in modeling anisotropic compact stars and exploring cosmic acceleration phenomena.