The distinctions between $\Lambda$CDM and $f(T)$ gravity according Noether symmetry

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 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. More important is that we find the significant differences between $\Lambda$CDM and $f(T)$ gravity. The $\Lambda$CDM model has also two additional symmetries and corresponding positive conserved quantities, except the two negative conserved quantities.

9 pages, 5 figures, 2 tables, typos corrected, Refs. added, accepted by EPJ-C

References in corpus (16)

• Planck 2013 results. XVI. Cosmological parameters
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Disappearing cosmological constant in f(R) gravity
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• Cosmological perturbations in f(T) gravity
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• Observational constraints on $f(T)$ theory
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Solar system constraints on f(T) gravity
• Observational information for f(T) theories and Dark Torsion
• Conformal transformation in $f(T)$ theories
• Static spherically symmetric perfect fluid solutions in $f(R)$ theories of gravity
• Noether symmetry in $f(R)$ cosmology

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• Scalar-Tensor Gravity Cosmology: Noether symmetries and analytical solutions
• Teleparallel dark energy model with a fermionic field via Noether symmetry
• Dynamical symmetries and observational constraints in scalar field cosmology
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• Noether symmetries and boundary terms in extended Teleparallel gravity cosmology
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• Scalar-Tensor Teleparallel Gravity With Boundary Term by Noether Symmetries
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• Inflation with F(T) Teleparallel Gravity
• Solar system tests for realistic $f(T)$ models with nonminimal torsion-matter coupling
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• Integrability from Point Symmetries in a family of Cosmological Horndeski Lagrangians
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