论文标题
高斯 - 邦奈特·切尔恩（Gauss-Bonnet-Chern）的平均宇宙
Gauss-Bonnet-Chern approach to the averaged Universe
论文作者
论文摘要
具有假定的暗能量和暗物质来源的宇宙学的标准模型可以被视为观察数据的相当成功的拟合模型。但是，该模型留下了这些深色组件开放的物理起源的问题。完全相对论的贡献可以通过大规模上的暗能量和较小尺度上的暗物质作用，可以通过对标准模型的概括来通过空间平均一般相对性中的不均匀宇宙来找到。空间平均3+1爱因斯坦方程是需要闭合条件的有效平衡方程。为了关闭，我们在这里探索拓扑约束。对于平均2+1模型宇宙，可直接获得结果。对于相关的3+1案例，我们采用一种基于概括为Lorentzian Pactimes的高斯 - 骨切尔纳特定理的方法，并实施一种三明治方法来获得空间平均属性。 3+1拓扑方法为我们提供了一个新的方程，将扩展张量的标量不变性与Weyl张量的标准联系起来。从中，我们得出了平均标态曲率和运动反应的一般演化方程，并讨论了有关平均方程层次结构级别的相关演化方程。我们还讨论了宇宙学歧管的拓扑特性与动态拓扑变化之间的关系，例如是由于黑洞的形成而产生的。
The standard model of cosmology with postulated dark energy and dark matter sources may be considered as a fairly successful fitting model to observational data. However, this model leaves the question of the physical origin of these dark components open. Fully relativistic contributions that act like dark energy on large scales and like dark matter on smaller scales can be found through generalization of the standard model by spatially averaging the inhomogeneous Universe within general relativity. The spatially averaged 3+1 Einstein equations are effective balance equations that need a closure condition. Heading for closure we here explore topological constraints. Results are straightforwardly obtained for averaged 2+1 model universes. For the relevant 3+1 case, we employ a method based on the Gauss-Bonnet-Chern theorem generalized to Lorentzian spacetimes and implement a sandwich approach to obtain spatial average properties. The 3+1 topological approach supplies us with a new equation linking evolution of scalar invariants of the expansion tensor to the norm of the Weyl tensor. From this we derive general evolution equations for averaged scalar curvature and kinematical backreaction, and we discuss related evolution equations on this level of the hierarchy of averaged equations. We also discuss the relation between topological properties of cosmological manifolds and dynamical topology change, e.g. as resulting from the formation of black holes.
