标题： 从无中创造宇宙作为宇宙学原理的替代方案 显示英文标题

标题： Creating a Universe from Nothing as an Alternative to the Cosmological Principle

摘要： 在宇宙学Robertson-Walker几何中，根据宇宙学原理，Weyl张量$C^{\mu\lambda\nu\kappa}$和Bach张量$W^{\mu\nu}=[2\nabla_{\kappa}\nabla_{\lambda}-R_{\lambda\kappa}]C^{\mu\lambda\nu\kappa}$都为零。 一般来说，在宇宙学背景的扰动中，波动的$\delta C^{\mu\lambda\nu\kappa}$或$\delta W^{\mu\nu}$都不会为零。 然而，即使$\delta C^{\mu\lambda\nu\kappa}$不为零，$\delta W^{\mu\nu}$也有可能为零。 在本文中，我们构建了一个具体的模型，其中这种情况成立。 该模型由一个在具有常负3曲率背景上波动的张量引力波组成。 该模型是精确可解的，仅由几何量组成，完全没有物质场（即，$G^{\mu\nu}=0$，$\delta G^{\mu\nu}=0$，$W^{\mu\nu}=0$，$\delta W^{\mu\nu}=0$，其中$G^{\mu\nu}$是爱因斯坦张量）。因此，该模型可以凭空创建，从无中创造宇宙因此成为宇宙学原理的一种替代原则。波动的引力波以可计算的方式对宇宙微波背景的温度各向异性做出贡献，我们提供了一种处理空间模式的简单解析方法，该方法基于空间模式叠加定理的使用。此外，我们还提供了一种基于带宽受限函数性质的各向异性处理方法。 显示英文摘要

摘要： In the cosmological Robertson-Walker geometry required of the cosmological principle both the Weyl tensor $C^{\mu\lambda\nu\kappa}$ and the Bach tensor $W^{\mu\nu}=[2\nabla_{\kappa}\nabla_{\lambda}-R_{\lambda\kappa}]C^{\mu\lambda\nu\kappa}$ vanish. In general, in perturbations around the cosmological background neither of the fluctuating $\delta C^{\mu\lambda\nu\kappa}$ or $\delta W^{\mu\nu}$ would vanish. However, it is possible for $\delta W^{\mu\nu}$ to vanish even as $\delta C^{\mu\lambda\nu\kappa}$ does not. In this paper we construct an explicit model in which this is the case. The model consists of a tensor gravitational wave fluctuating around a background with a constant negative 3-curvature. The model is exactly solvable and consists purely of geometric quantities with no matter fields at all (i.e., $G^{\mu\nu}=0$, $\delta G^{\mu\nu}=0$, $W^{\mu\nu}=0$, $\delta W^{\mu\nu}=0$, where $G^{\mu\nu}$ is the Einstein tensor). The model can thus be created out of nothing, with creating a universe from nothing thus being an alternative principle to the cosmological principle. The fluctuating gravitational wave contributes to the temperature anisotropy in the cosmic microwave background in a calculable manner, for which we provide a simple analytic way of treating spatial modes that is based on the use of a spatial mode addition theorem. In addition, we provide a treatment of the anisotropy that is based on properties of bandwidth limited functions.