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arXiv · 2307.11475

Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity

R. J. van den Hoogen·A. A. Coley·D. D. McNutt
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Abstract

Symmetry assumptions on the geometrical framework have provided successful mechanisms to develop physically meaningful solutions to many problems. In tele-parallel gravity, invariance of the frame and spin-connection under a group of motions defines an affine symmetry group. Here, we assume there exists a three-dimensional group of affine symmetries acting simply transitively on a spatial hypersurface and that this group of symmetry actions defines our affine frame symmetry group. We determine the general form of the co-frame and spin connection for each spatially homogeneous Bianchi type. We then construct the corresponding field equations for $f(T)$ tele-parallel gravity. We show that if the symmetry group is of Bianchi type A ($I$, $II$, $VI_0$, $VII_0$, $VIII$ or $IX$) then there exists a co-frame/spin connection pair that is consistent with the antisymmetric part of the field equations of $f(T)$ tele-parallel gravity. For those geometries having a Bianchi type B symmetry group ($IV$, $V$, $VI_h$, $VII_h$), we find that in general these geometries are inconsistent with the antisymmetric part of the $f(T)$ tele-parallel gravity field equations unless the theory reduces to an analog of General Relativity with a cosmological constant.

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R. J. van den Hoogen, A. A. Coley, D. D. McNutt. 2023-07-21. Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity. https://doi.org/10.1088/1475-7516%2F2023%2F10%2F042

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