Spatially Homogeneous Teleparallel Gravity: Bianchi I

Abstract

Using a recently developed algorithm that chooses preferred coordinates and a preferred co-frame, we will determine the completely general Bianchi type I teleparallel geometry. In using this algorithm, any remaining gauge freedom is allocated to the choice of spin connection. We then solve the symmetry constraints placed on the spin connection to derive a general class of Bianchi type I teleparallel geometries. We find that this general class of Bianchi type I teleparallel geometries breaks naturally into two sub-classes. We then illustrate some simple power-law solutions in $F(T)$ teleparallel gravity for each case to illustrate the differences.

arXiv comment18 pages

References in corpus (41)

• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• Modified Gravity and Cosmology
• Extended Theories of Gravity
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• A 2.4% Determination of the Local Value of the Hubble Constant
• f(T) teleparallel gravity and cosmology
• Modified teleparallel gravity: inflation without inflaton
• Teleparallel Gravity: From Theory to Cosmology
• The covariant formulation of f(T) gravity
• Modified teleparallel theories of gravity
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Good and bad tetrads in f(T) gravity
• Non trivial frames for f(T) theories of gravity and beyond
• Metric-affine approach to teleparallel gravity
• Cosmological Solutions of $f(T)$ Gravity
• On the covariance of teleparallel gravity theories
• Numerical Approaches to Spacetime Singularities
• Anisotropic Universe Models in f(T) Gravity
• Covariant formulation of scalar-torsion gravity
• The past attractor in inhomogeneous cosmology
• F(T) Models within Bianchi Type I Universe
• Classification of the Weyl Tensor in Higher Dimensions and Applications
• Regularizing role of teleparallelism
• Covariance properties and regularization of conserved currents in tetrad gravity
• Spin Connection and Renormalization of Teleparallel Action
• Teleparallel theories of gravity as analogue of non-linear electrodynamics
• Locally Rotationally Symmetric Bianchi Type-I cosmological model in $f(T)$ gravity: from early to Dark Energy dominated universe
• Holographic Renormalization in Teleparallel Gravity
• Stability of the Kasner Universe in f(T) Gravity
• Symmetry and Equivalence in Teleparallel Gravity
• Bianchi type-I, type-III and Kantowski-Sachs solutions in f(T) gravity
• Spacetime and observer space symmetries in the language of Cartan geometry
• Kantowski-Sachs Universe Models in $f(T)$ Theory of Gravity
• A frame based approach to computing symmetries with non-trivial isotropy groups
• Symmetric Teleparallel Geometries
• On Kasner solution in Bianchi I $f(T)$ cosmology
• Noether gauge symmetry for the Bianchi type I model in f(T) gravity
• Anisotropic cosmological dynamics in $f(T)$ gravity in the presence of a perfect fluid
• Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity
• Bianchi I cosmological solutions in teleparallel gravity
• Teleparallel Geometry with a Single Affine Symmetry

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• Anisotropic Cosmology in the Local Limit of Nonlocal Gravity
• More on Bianchi I spacetimes and f(T) gravity