Diagnostics for generalized power-law torsion–matter coupling f(T) model
The currently accelerated expansion of our universe is unarguably one of the most intriguing problems in today’s physics research. Two realistic nonminimal torsion–matter coupling [Formula: see text] models have been established and studied in our previous papers [C. J. Feng, F. F. Ge, X. Z. Li, R. H. Lin and X. H. Zhai, Phys. Rev. D 92 (2015) 104038; R. H. Lin, X. H. Zhai and X. Z. Li, Eur. Phys. J. C 77 (2017) 504] aiming to explain this “dark energy” problem. In this paper, we study the generalized power-law torsion–matter coupling [Formula: see text] model. Dynamical system analysis shows that the three expansion phases of the universe, i.e. the radiation-dominated era, the matter-dominated era and the dark energy-dominated era, can all be reproduced in this generalized model. By using the statefinder and [Formula: see text] diagnostics, we find that the different cases of the model can be distinguished from each other and from other dark energy models such as the two models in our previous papers, [Formula: see text]CDM, quintessence and Chaplygin gas. Furthermore, the analyses also show that all kinds of generalized power-law torsion–matter coupling model are able to cross the [Formula: see text] divide from below to above, which is a realization of quintom scenario. The decrease of the energy density resulting from the crossing of [Formula: see text] will make the catastrophic fate of the universe avoided and a de Sitter expansion fate in the future will be approached.