Reconstruction of $f(T)$-gravity in the absence of matter

Abstract

We derive an exact $f(T)$ gravity in the absence of ordinary matter in Friedmann-Robertson-Walker (FRW) universe, where $T$ is the teleparallel torsion scalar. We show that vanishing of the energy-momentum tensor ${\mathcal{T}}^{\mu \nu }$ of matter does not imply vanishing of the teleparallel torsion scalar, in contrast to general relativity, where the Ricci scalar vanishes. The theory provides an exponential (inflationary) scale factor independent of the choice of the sectional curvature. In addition, the obtained $f(T)$ acts just like cosmological constant in the flat space model. Nevertheless, it is dynamical in non-flat models. In particular, the open universe provides a decaying pattern of the $f(T)$ contributing directly to solve the fine-tuning problem of the cosmological constant. The equation of state (EoS) of the torsion vacuum fluid has been studied in positive and negative Hubble regimes. We study the case when the torsion is made of a scalar field (tlaplon) which acts as torsion potential. This treatment enables to induce a tlaplon field sensitive to the symmetry of the spacetime in addition to the reconstruction of its effective potential from the $f(T)$ theory. The theory provides six different versions of inflationary models. The real solutions are mainly quadratic, the complex solutions, remarkably, provide Higgs-like potential.

14 pages, 6 Figures, 2 Tables. v3: The title has been changed in addition to other minor changes

References in corpus (26)

• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• On Born-Infeld Gravity in Weitzenbock spacetime
• Teleparallel equivalent of Gauss-Bonnet gravity and its modifications
• Generalizations of teleparallel gravity and local Lorentz symmetry
• Solar system constraints on f(T) gravity
• Nonminimal torsion-matter coupling extension of f(T) gravity
• Conformal transformation in $f(T)$ theories
• Dynamical behavior in $f(T,T_G)$ cosmology
• Exact charged black-hole solutions in D-dimensional f(T) gravity: torsion vs curvature analysis
• Cosmological applications of $F(T,T_G)$ gravity
• Constraining f(T) gravity in the Solar System
• The Hidden Flat Like Universe: Starobinsky-like inflation induced by f(T) gravity
• Charged Axially Symmetric Solution and Energy in Teleparallel Theory Equivalent to General Relativity
• Nonsingular bouncing cosmologies in light of BICEP2
• Schwarzschild solution in extended teleparallel gravity
• Kerr geometry in f(T) gravity
• Linear Connections and Curvature Tensors in the Geometry of Parallelizable Manifolds
• Revisiting the holographic dark energy in a non-flat universe: alternative model and cosmological parameter constraints
• Born-Infeld and Charged Black Holes with non-linear source in $f(T)$ Gravity
• $f(T)$ non-linear massive gravity and the cosmic acceleration
• An Ap-Structure with Finslerian Flavor: I
• The vacuum energy crisis
• Dark energy as a kinematic effect

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• Constant-roll Inflation in $f(T)$ Teleparallel Gravity
• Bounce inflation in $f(T)$ Cosmology: A unified inflaton-quintessence field
• Generalized teleparallel cosmology and initial singularity crossing
• Higgs inflation and teleparallel gravity
• Reconstructing inflation in scalar-torsion $f(T,\varphi )$ gravity
• On the Viability of the Intermediate Inflation Scenario with $F(T)$ Gravity
• The Hidden Flat Like Universe II: Quasi inverse power law inflation by $f(T)$ gravity
• Generic Phase Portrait Analysis of the Finite-time Singularities and Generalized Teleparallel Gravity
• On the Expanding Phase of a Singular Bounce and Intermediate Inflation: The Modified Gravity Description
• Magnetic black holes in 4$D$ Einstein--Gauss--Bonnet massive gravity coupled to nonlinear electrodynamics
• An innovative black hole solution and thermodynamic properties in higher-order curvature gravity with a scalar field
• Charged analog of anisotropic dark energy star in Rastall gravity