Observational constraints on $f(T)$ theory

TL;DR

This paper investigates $f(T)$ gravity models as alternatives to dark energy for cosmic acceleration, analyzing their theoretical properties and observational constraints, and comparing their fit to data with the standard $\\Lambda$CDM model.

Contribution

It performs the first statefinder and $Om(z)$ diagnostics on specific $f(T)$ models and constrains them with recent observational data, highlighting differences from previous claims and the standard model.

Findings

Both models cannot cross the phantom divide line.

Observational data favor the $\\Lambda$CDM model over the $f(T)$ models.

Data suggest a phantom-like dark energy with Sne Ia alone, but quintessence-like with combined data.

Abstract

The $f(T)$ theory, which is an extension of teleparallel, or torsion scalar $T$, gravity, is recently proposed to explain the present cosmic accelerating expansion with no need of dark energy. In this Letter, we first perform the statefinder analysis and $Om(z)$ diagnostic to two concrete $f(T)$ models, i.e., $f(T)=\alpha (-T)^n$ and $f(T)=-\alpha T(1-e^{p {T_0}/T})$, and find that a crossing of phantom divide line is impossible for both models. This is contrary to an existing result where a crossing is claimed for the second model. We, then, study the constraints on them from the latest Union 2 Type Ia Supernova (Sne Ia) set, the baryonic acoustic oscillation (BAO), and the cosmic microwave background (CMB) radiation. Our results show that at the 95% confidence level $\Omega_{m0}=0.272_{-0.032}^{+0.036}$, $n=0.04_{-0.33}^{+0.22}$ for Model 1 and $\Omega_{m0}=0.272_{-0.034}^{+0.036}$, $p=-0.02_{-0.20}^{+0.31}$ for Model 2. A comparison of these two models with the $\Lambda$CDM by the $\chi^2_{Min}/dof$ (dof: degree of freedom) criterion indicates that $\Lambda$CDM is still favored by observations. We also study the evolution of the equation of state for the effective dark energy in the theory and find that Sne Ia favors a phantom-like dark energy, while Sne Ia + BAO + CMB prefers a quintessence-like one.