We investigate the cosmological implications of torsion–boundary gravity with explicit matter coupling in f(T, B, 𝒯) gravity. The purpose is to examine if such couplings offer observationally viable extensions to standard cosmology. Focusing on linear and power-law model realizations, we derive the modified Friedmann equations and analyze the resulting background dynamics. Using a combination of late-time datasets—including Cosmic Chronometers, Type Ia Supernovae, and Baryon Acoustic Oscillations—we perform a joint likelihood analysis to constrain the model parameters. Our results show that both f(T, B, 𝒯) models remain compatible with current observations and effectively reduce to the ΛCDM paradigm in their appropriate parameter limits. While the power-law model exhibits mild dynamical deviations at intermediate redshifts, it remains statistically indistinguishable from the standard cosmological model. We conclude that f(T, B, 𝒯) gravity represents a viable and robust extension of torsional modified gravity, motivating further study of non-minimal matter–geometry couplings in cosmology.
Al-Omar et al. (Mon,) studied this question.