Abstract

Nowadays, according to the observational evidence, the curvature parameter of the universe is neglected, and a spatially flat FLRW model is on the top of interest for cosmologists. However, due to some discrepancies between the \(\Lambda\)CDM model, anticipations and observations, one may think out the curvature parameter as the solution even though it may be very small. So, in this article we investigate the eras in which the curvature influence was or is more significant. In addition, a geometric interpretation of the Hubble parameter is put forward. We find that the Hubble parameter is more appropriate to be defined as the mean curvature of the spatial section of the universe because the concept of the scale factor in a inhomogeneous universe is not precisely clear. Moreover, we realize that by employing linear perturbations, two principal curvatures of the absolute space change into what depends on the local Hubble parameter.

中文翻译：

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宇宙学中内在和外在曲率的印记

摘要

如今，根据观测证据，宇宙的曲率参数被忽略了，空间平坦的FLRW模型成为宇宙学家最感兴趣的。但是，由于\(\Lambda\)CDM 模型、预期和观察，即使曲率参数可能非常小，也可以将其视为解决方案。因此，在本文中，我们调查曲率影响曾经或更为显着的时代。此外，还提出了哈勃参数的几何解释。我们发现哈勃参数更适合定义为宇宙空间截面的平均曲率，因为非均匀宇宙中比例因子的概念并不十分清楚。此外，我们意识到通过使用线性扰动，绝对空间的两个主要曲率会变成取决于局部哈勃参数的曲率。