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2020

Complete classification of cosmological teleparallel geometries

Hohmann, Manuel

Understand

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.