Recently a $f(T)$ gravity based on the modification of the teleparallel gravity was proposed to explain the accelerated expansion of the universe without the need of dark energy. We use observational data from Type Ia Supernovae, Baryon Acoustic Osci
llations, and Cosmic Microwave Background to constrain this $f(T)$ theory and reconstruct the effective equation of state and the deceleration parameter. We obtain the best-fit values of parameters and find an interesting result that the $f(T)$ theory considered here allows for the accelerated Hubble expansion to be a transient effect.
We consider constraints on generalized tachyon field (GTF) models from latest observational data (including 182 gold SNIa data, the shift parameter, and the acoustic scale). We obtain at 68.3% confidence level $Omega_{rm m}=0.37pm0.01$, $k_0=0.09^{+0
.04}_{-0.03}$, $alpha=1.8^{+7.4}_{-0.7}$ (the best-fit values of the parameters) and $z_{q=0}sim 0.47-0.51$ (the transitional redshift) for GTF as dark energy component only; $k_0=0.21^{+0.20}_{-0.18}$, $alpha=0.57pm0.01$ and $z_{q=0}sim 0.49-0.68$ for GTF as unification of dark energy and dark matter. In both cases, GTF evolves like dark matter in the early universe. By applying model-comparison statistics and test with independent $H(z)$ data, we find GTF dark energy scenario is favored over the $Lambda$CDM model, and the $Lambda$CDM model is favored over GTF unified dark matter by the combined data. For GTF as dark energy component, the fluctuations of matter density is consistent with the growth of linear density perturbations. For GTF unified dark matter, the growth of GTF density fluctuations grow more slowly for $ato1$, meaning GTF do not behave as classical $Lambda$CDM scenarios.
