Han Dong, Jiaxin Wang, Xinhe Meng
Noether's theory offers us a useful tool to research the conserved quantities and symmetries of the modified gravity theories, among which the f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. By the Noether symmetry approach, we investigate the power-law, exponential and polynomial forms of f(T) theories with corresponding conserved quantities and symmetries. All forms of f(T) concerned in this work possess the time translational symmetry, which is related with energy condition or Hamilton constraint. And we find out that the performances of the power-law and exponential forms are not pleasing. It is rational adding a linear term $T$ to $T^n$ as the most efficient amendment to resemble the teleparallel gravity or General Relativity on small scales, ie., the scale of the solar system. The corresponding Noether symmetry indicates that only time translational symmetry remains. Through numerically calculations and observational data-sets constraining, the optimal form $\alpha T + \beta T^{-1}$ is obtained, whose cosmological solution resembles the standard $\Lambda$CDM best with lightly reduced cosmic age which can be alleviated by introducing another $T^m$ term. Proper constraints on the ratio $\beta/\alpha$ are also given, which can be converted into constraints on the ratio of the magnitude of torsion between large and small scales.
View original:
http://arxiv.org/abs/1304.6587
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