论文标题
宇宙学静电平行的几何形状的完整分类
Complete classification of cosmological teleparallel geometries
论文作者
论文摘要
我们考虑宇宙学对称性的概念，即空间均匀性和各向同性，在远程平行的重力和几何学领域，并提供了所有同质和各向同性远程的几何形状的完整分类。我们通过独立采用三种不同的方法来明确构建这些几何形状，并证明它们都导致了同一类别的几何形状。此外，我们得出它们的性质，例如扭转张量及其不可约合的分解，以及时间坐标变化下的转换行为，并得出许多远程平行性理论的最通用的宇宙学场方程。除均匀性和各向同性外，我们还将宇宙对称性的概念扩展到还包括空间反射，并发现这进一步限制了可能的触发线几何形状。这项工作回答了电视剧宇宙学中的一个重要问题，迄今为止，仅知道宇宙学对称解决方案的特定示例，但尚不清楚是否可以构建进一步的解决方案。
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.
