We show that the big bang is a coordinate singularity for a large class of $k = -1$ inflationary FLRW spacetimes which we have dubbed 'Milne-like.' By introducing a new set of coordinates, the big bang appears as a past boundary of the universe where the metric is no longer degenerate -- a result which has already been investigated in the context of vacuum decay [12]. We generalize their results and approach the problem from a more mathematical perspective. Similar to how investigating the geometrical properties of the $r = 2m$ event horizon in Schwarzschild led to a better understanding of black holes, we believe that investigating the geometrical properties of the big bang coordinate singularity for Milne-like spacetimes could lead to a better understanding of cosmology. We show how the mathematics of these spacetimes may help illuminate certain issues associated with dark energy, dark matter, and the universe's missing antimatter.

中文翻译：

---

大爆炸是 $$k = -1$$k=-1 暴涨 FLRW 时空的坐标奇点

我们证明了大爆炸是一大类 $k = -1$ 暴胀 FLRW 时空的坐标奇点，我们称之为“类米尔恩”。通过引入一组新的坐标，大爆炸作为宇宙的过去边界出现，在那里度量不再退化——这一结果已经在真空衰变的背景下进行了研究 [12]。我们概括了他们的结果，并从更数学的角度来解决问题。类似于研究 Schwarzschild 中 $r = 2m$ 事件视界的几何特性如何导致更好地理解黑洞，我们相信研究类似米尔恩时空的大爆炸坐标奇点的几何特性可以导致更好的理解。对宇宙学的理解。