Constraining $f(T,\mathcal{T})$ gravity models using type Ia supernovae

We present an analysis of an $f(T,\mathcal{T})$ extension of the Teleparallel Equivalent of General Relativity, where $T$ denotes the torsion and $\mathcal{T}$ the trace of the energy-momentum tensor. This extension includes non–minimal couplings between torsion and matter. In particular, we construct two specific models that recover the usual continuity equation, namely, $f(T,\mathcal{T})=T+g(\mathcal{T})$ and $f(T, $\mathcal{T}$)=T\times g($\mathcal{T}$)$. We then constrain the parameters of each model by fitting the predicted distance modulus to that measured from type Ia supernovae, and find that both models can reproduce the late–time cosmic acceleration. We also observe that one of the models satisfies well the observational constraints and yields a goodness–of–fit similar to the $\mathrm{\Lambda }$CDM model, thus demonstrating that $f(T,\mathcal{T})$ gravity theory encompasses viable models that can be an alternative to $\mathrm{\Lambda }$CDM.