Testing the viability of $f(T, \mathcal{T})$ gravity models via effective equation of state constraints

This paper rigorously examines the potential of the $f(T, \mathcal{T})$ theory as a promising framework for understanding the dark sector of the universe, particularly in relation to cosmic acceleration. The $f(T, \mathcal{T})$ theory extends gravitational dynamics by incorporating both the torsion scalar $T$ and the trace of the energy-momentum tensor $\mathcal{T}$. Further, we explore the functional form $f(T, \mathcal{T}) = T + \beta \mathcal{T}$, where $\beta$ is a free parameter that modulates the matter's influence on spacetime evolution. To evaluate this model, we employ an effective EoS parameter dependent on redshift $z$, to solve the field equations and analyze the evolution of the Hubble parameter $H(z)$. Using a joint dataset ($H(z)+Pantheon^+$) and the Markov Chain Monte Carlo (MCMC) method with Bayesian analysis, we obtain the best-fit parameter values: $H_0 = 68.04 \pm 0.64$, $\beta = 0.14 \pm 0.17$, and $\gamma = 0.96^{+0.38}_{-0.69}$, which align well with current observational data. Our findings indicate a deceleration parameter of $q_0 = -0.51$, supporting a present-day accelerated expansion phase, with a transition redshift $z_t = 0.57$ marking the universe's shift from deceleration to acceleration. Moreover, we confirm a positive cosmic fluid energy density, reinforcing stability, and find an EoS parameter value of $\omega_0 = -0.76$, consistent with quintessence-driven acceleration. These results underscore the viability of $f(T, \mathcal{T})$ as a robust framework for addressing the accelerating universe and dark energy dynamics, paving the way for future investigations into its cosmological implications.