Cosmological Solutions of $f(T)$ Gravity

Abstract

In the cosmological scenario in $f\left(T\right)$ gravity, we find analytical solutions for an isotropic and homogeneous universe containing a dust fluid and radiation and for an empty anisotropic Bianchi I universe. The method that we apply is that of movable singularities of differential equations. For the isotropic universe, the solutions are expressed in terms of a Laurent expansion, while for the anisotropic universe we find a family of exact Kasner-like solutions in vacuum. Finally, we discuss when a nonlinear $f\left(T\right)$-gravity theory provides solutions for the teleparallel equivalence of general relativity and derive conditions for exact solutions of general relativity to solve the field equations of an $f(T)$ theory.

arXiv comment13 pages, accepted for publication by Phys. Rev. D

References in corpus (27)

• Generalized Chaplygin Gas, Accelerated Expansion and Dark Energy-Matter Unification
• f(T) teleparallel gravity and cosmology
• Dark torsion as the cosmic speed-up
• Modified teleparallel gravity: inflation without inflaton
• Einstein's Other Gravity and the Acceleration of the Universe
• Evolution of the Scale Factor with a Variable Cosmological Term
• f(T) Gravity and local Lorentz invariance
• Observational constraints on $f(T)$ theory
• Cosmography in f(T)-gravity
• Good and bad tetrads in f(T) gravity
• Torsion Gravity: a Reappraisal
• Observational information for f(T) theories and Dark Torsion
• Spherically symmetric static spacetimes in vacuum f(T) gravity
• Cosmology with massive neutrinos coupled to dark energy
• New Schwarzschild-like solutions in f(T) gravity through Noether symmetries
• Exact charged black-hole solutions in D-dimensional f(T) gravity: torsion vs curvature analysis
• Anisotropic Universe Models in f(T) Gravity
• Noether symmetries and analytical solutions in f(T)-cosmology: A complete study
• $f(T)$ cosmology via Noether symmetry
• Further Exact Cosmological Solutions to Higher-Order Gravity Theories
• Exact cosmological solutions of scale-invariant gravity theories
• Constraining f(T) gravity in the Solar System
• A New Solution of The Cosmological Constant Problems
• Linear growth in power law $f(T)$ gravity
• A Testable Solution of the Cosmological Constant and Coincidence Problems
• On The Existence Of Anisotropic Cosmological Models In Higher-Order Theories Of Gravity
• Bianchi type-I, type-III and Kantowski-Sachs solutions in f(T) gravity

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