Constraining f(T,T) gravity models using type Ia supernovae

We present an analysis of an f(T,T) extension of the Teleparallel Equivalent of General Relativity, where T denotes the torsion and T denotes the trace of the energy-momentum tensor. This extension includes nonminimal couplings between torsion and matter. In particular, we construct two specific models that recover the usual continuity equation, namely, f(T,T) = T + g(T) and f(T,T) = T x g(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 Lambda CDM model, thus demonstrating that f(T,T) gravity theory encompasses viable models that can be an alternative to Lambda CDM.