Complete classification of cosmological teleparallel geometries

Abstract

We consider the notion of cosmological symmetry, i.e., spatial homogeneity and isotropy, in the field of teleparallel gravity and geometry, and provide a complete classification of all homogeneous and isotropic teleparallel geometries. We explicitly construct these geometries by independently employing three different methods, and prove that all of them lead to the same class of geometries. Further, we derive their properties, such as the torsion tensor and its irreducible decomposition, as well as the transformation behavior under change of the time coordinate, and derive the most general cosmological field equations for a number of teleparallel gravity theories. In addition to homogeneity and isotropy, we extend the notion of cosmological symmetry to also include spatial reflections, and find that this further restricts the possible teleparallel geometries. This work answers an important question in teleparallel cosmology, in which so far only particular examples of cosmologically symmetric solutions had been known, but it was unknown whether further solutions can be constructed.

37 pages, no figures; to appear in a Special Issue of the International Journal of Geometric Methods in Modern Physics, based on a presentation at the Teleparallel Gravity Workshop 2020 in Tartu

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• Dark torsion as the cosmic speed-up
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Cited by in corpus (22)

• Teleparallel Gravity: From Theory to Cosmology
• Covariant formulation of f(Q) theory
• General covariant symmetric teleparallel cosmology
• Perturbations in Non-Flat Cosmology for $f(T)$ gravity
• Homogeneous and isotropic cosmology in general teleparallel gravity
• Teleparallel axions and cosmology
• A frame based approach to computing symmetries with non-trivial isotropy groups
• Exploring the stability of $f(Q)$ cosmology near general relativity limit with different connections
• Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity
• Equivalence of $f(Q)$ cosmology with quintom-like scenario: the phantom field as effective realization of the non-trivial connection
• Teleparallel gravity
• Spherically symmetric teleparallel geometries
• General Effective Field Theory of Teleparallel Gravity
• Gravitational wave birefringence in spatially curved teleparallel cosmology
• Stability of symmetric teleparallel scalar-tensor cosmologies with alternative connections
• Teleparallel Robertson-Walker geometries and applications
• Teleparallel Geometry with a Single Affine Symmetry
• Teleparallel dark energy in a nonflat universe
• Can an Extra Degree of Freedom in Scalar-Tensor Non-Metricity Gravity Account for the Evolution of the Universe?
• Spatially homogeneous teleparallel spacetimes with four-dimensional groups of motions
• Global portraits of nonminimal teleparallel inflation
• Revisiting a parity violating gravity model without ghost instability: Local Lorentz covariance