Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity
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arXiv
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| Format: | Preprint |
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2023
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| author | Hoogen, R. J. van den Coley, A. A. McNutt, D. D. |
| author_facet | Hoogen, R. J. van den Coley, A. A. McNutt, D. D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11475 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity Hoogen, R. J. van den Coley, A. A. McNutt, D. D. General Relativity and Quantum Cosmology 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. |
| title | Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2307.11475 |