Eur. Phys. J. C (2013) 73: 2543
https://doi.org/10.1140/epjc/s10052-013-2543-2

Regular Article - Theoretical Physics

The distinctions between ΛCDM and f(T) gravity according to Noether symmetry

¹ Department of physics, Nankai University, Tianjin, 300071, China
² Kavli Institute of Theoretical Physics China, CAS, Beijing, 100190, China

^* e-mail: donghan@mail.nankai.edu.cn

Received: 27 June 2013
Revised: 3 August 2013
Published online: 28 August 2013

Abstract

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 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. All forms of f(T) concerned in this work possess the time translational symmetry, which is related with energy condition or Hamilton constraint. In addition, we find 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, i.e., 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 αT+βT ⁻¹ is obtained, whose cosmological solution resembles the standard ΛCDM best with lightly reduced cosmic age which can be alleviated by introducing another T ^m term. More important is that we find the significant differences between ΛCDM and f(T) gravity. The ΛCDM model has also two additional symmetries and corresponding positive conserved quantities, except the two negative conserved quantities.