Diagnostics for generalized power-law torsion-matter coupling $f(T)$ model

TL;DR

This paper introduces a generalized power-law torsion-matter coupling $f(T)$ model that can reproduce all major cosmic expansion phases and distinguish itself from other dark energy models, potentially avoiding catastrophic future scenarios.

Contribution

It develops a new generalized power-law $f(T)$ model and demonstrates its ability to replicate cosmic history and differentiate from other dark energy models using diagnostic tools.

Findings

Reproduces radiation, matter, and dark energy dominated eras.

Can cross the $w=-1$ divide, avoiding catastrophic fate.

Distinguishable from $ ext{Lambda}$CDM, quintessence, and Chaplygin gas.

Abstract

The currently accelerated expansion of our Universe is unarguably one of the most intriguing problems in today's physics research. Two realistic non-minimal torsion-matter coupling $f(T)$ models have been established and studied in our previous papers [Phys. Rev. D92, 104038(2015) and Eur. Phys. J. C77, 504(2017)] aiming to explain this "dark energy" problem. In this paper, we study the generalized power-law torsion-matter coupling $f(T)$ 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 $Om$ 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, $\Lambda$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 $w=-1$ divide from below to above, thus the decrease of the energy density resulting from the crossing of $w$ will make the catastrophic fate of the Universe avoided and a de Sitter expansion fate in the future will be approached.