论文标题
基于观察者的宇宙模型不变性
Observer-based invariants for cosmological models
论文作者
论文摘要
我们考虑了四维重力理论中宇宙学模型的等效问题。宇宙学模型被认为是三重$（m，{\ bf g}，{\ bf u}）$，由时空$（m，{\ bf g}）$组成，而优选的正常化的时间段的矢量字段$ {\ bf u} $ confents $ {\ bf u} $与基本生态观察者的祝贺相切。我们通过限制适用于$ {\ bf u} $的框架，包括$ {\ bf u} $的协变量衍生物以及Riemann Tensor及其协证衍生物。为了固定框架，我们使用数量相对于基本观察者，例如各向异性压张量，能量通量矢量，Weyl张量的电和磁性部分以及$ {\ bf u} $的运动量数量。这提供了一种更简单的方法来构建相对于完全表征模型的基本观察者的不变性列表，而与坐标无关。作为算法的例证，我们考虑了从一般相对论中考虑的几种众所周知的宇宙学模型。
We consider the equivalence problem for cosmological models in four-dimensional gravity theories. A cosmological model is considered as a triple $(M, {\bf g},{\bf u})$ consisting of a spacetime $(M, {\bf g})$ and a preferred normalized time-like vector field ${\bf u}$ tangent to a congruence of fundamental observers. We introduce a modification of the Cartan-Karlhede algorithm by restricting to frames adapted to ${\bf u}$ and including the covariant derivatives of ${\bf u}$ along with the Riemann tensor and its covariant derivatives. To fix the frame we make use of quantities relative to the fundamental observers, such as the anisotropic pressure tensor, energy flux vector, electric and magnetic parts of the Weyl tensor and the kinematical quantities of ${\bf u}$. This provides a simpler way to construct a list of invariants relative to the fundamental observers that completely characterizes the model, independent of coordinates. As an illustration of the algorithm, we consider several well-known cosmological models from General Relativity.
