论文标题
扩展是否对空间曲率视而不见？
Is expansion blind to the spatial curvature?
论文作者
论文摘要
在[Arxiv：2204.13980]中，我们提出并激发了爱因斯坦方程作为宇宙拓扑的修改，其函数是双方连接理论的形式。新方程具有与第二个非动力参考连接相关的附加“拓扑术语”，并作为时空拓扑的函数选择。在本文中，我们分析了这种修饰的宇宙学的后果。首先，我们表明扩展对这个新理论中的空间曲率视而不见，即扩展定律不再具有空间曲率参数（即$ω_ {\ not = k} = 1，\\ forall \ forall \ forall \，ω_k$），而该曲率仍然存在于距离的评估中。其次，我们得出了该均匀解决方案的一阶扰动。与一般相对论相比，参考连接的另外两个不变变量存在：标量和矢量模式，均由宇宙流体的剪切作出。最后，我们与观察结果面对这一模型。 $λ$ CDM模型的差异尤其可以忽略不计，尤其是哈勃和弯曲张力仍然存在。然而，由于两个模型之间的主要区别是背景空间曲率对动力学的影响，因此该参数的度量的精确度提高了，这可能使我们能够在观察上区分它们。
In [arXiv:2204.13980], we proposed and motivated a modification of the Einstein equation as a function of the topology of the Universe in the form of a bi-connection theory. The new equation features an additional "topological term" related to a second non-dynamical reference connection and chosen as a function of the spacetime topology. In the present paper, we analyse the consequences for cosmology of this modification. First, we show that expansion becomes blind to the spatial curvature in this new theory, i.e. the expansion laws do not feature the spatial curvature parameter anymore (i.e. $Ω_{\not= K} = 1, \ \forall \, Ω_K$), while this curvature is still present in the evaluation of distances. Second, we derive the first order perturbations of this homogeneous solution. Two additional gauge invariant variables coming from the reference connection are present compared with general relativity: a scalar and a vector mode, both sourced by the shear of the cosmic fluid. Finally, we confront this model with observations. The differences with the $Λ$CDM model are negligible, in particular, the Hubble and curvature tensions are still present. Nevertheless, since the main difference between the two models is the influence of the background spatial curvature on the dynamics, an increased precision on the measure of that parameter might allow us to observationally distinguish them.
