Unified dark sectors in scalar-torsion theories of gravity

We present a unified description of the matter and dark energy epochs using a class of scalar-torsion theories. We provide a Hamiltonian description, and by applying Noether's theorem and requiring the field equations to admit linear-in-momentum conservation laws, we obtain two specific classes of scalar-field potentials. First, we extract analytic solutions and perform a detailed dynamical analysis. We show that the system possesses critical points that correspond to scaling solutions in which the effective, total equation-of-state parameter is close to zero and points in which it is equal to the value -1; the equation of state of the cosmological constant. Therefore, during evolution, the Universe remains for sufficiently long at the epoch corresponding to dust-matter domination, while at later times it enters the accelerated epoch and eventually results in the de Sitter phase. Finally, in contrast to other unified scenarios, such as Chaplygin gas-based models and Horndeski-based constructions, the present scenario is free from instabilities and pathologies at the perturbative level.