arXiv 1709.033142017-09gr-qchep-thmath-phmath.GTmath.MP

如何从小的奇异R^4中获得宇宙学常数

How to obtain a cosmological constant from small exotic R^4

T. Asselmeyer-Maluga, J. Krol

备注：: 36 pages, 5 figures, substantial changes, the value of the cosmological constant in agreement with measurements, accepted in Physics of the Dark Universe
发表信息：: Physics of the Dark Universe Volume 19, March 2018, Pages 66-77
DOI：: 10.1016/j.dark.2017.12.002

摘要：

本文从低维微分拓扑学出发，应用一定的技巧，确定了作为拓扑不变量的宇宙学常数。我们使用嵌入到标准$\mathbb{R}^{4}$中的小型外来$R^{4}$。任何奇异的$R^4$都是具有必要的非零曲率张量的黎曼光滑流形。为了确定不变的一部分，这样的曲率，我们处理一个典型的建设$R^4$，它出现在复杂的表面$K3\#\overline{CP(2)}$的一部分。这样的$R^{4}$的承认双曲几何。这一事实大大简化了计算，并加强了表达式的刚性。特别是，我们解释了小的宇宙学常数的值组成的（自然）拓扑不变的组合。最后，宇宙学常数似乎是一个拓扑学支持的量。

英文摘要：

In this paper we determine the cosmological constant as a topological invariant by applying certain techniques from low dimensional differential topology. We work with a small exotic $R^{4}$ which is embedded into the standard $\mathbb{R}^{4}$. Any exotic $R^4$ is a Riemannian smooth manifold with necessary non-vanishing curvature tensor. To determine the invariant part of such curvature we deal with a canonical construction of $R^4$ where it appears as a part of the complex surface $K3\#\overline{CP(2)}$. Such $R^{4}$'s admit hyperbolic geometry. This fact simplifies significantly the calculations and enforces the rigidity of the expressions. In particular, we explain the smallness of the cosmological constant with a value consisting of a combination of (natural) topological invariant. Finally, the cosmological constant appears to be a topologically supported quantity.

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