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Advances in international applied mathematics. 2020; 2: (1) 2; DOI: 10.12208/j.aam.20200002.

Dynamical Constraints on the Cosmological Parameters
宇宙结构参数的动力学限制

作者: 辜英求*

复旦大学数学科学学院

*通讯作者:辜英求,单位:复旦大学数学科学学院;

引用本文: 辜英求. 宇宙结构参数的动力学限制[J]. 国际应用数学进展, 2020, 2(1) : 14-20.
Published: 2020-05-14

摘要

在宇宙学中,宇宙曲率K和宇宙学常数Λ是两个最重要的参数,其值对宇宙的演化有重大的影响。本文在正能量密度和负初始压力的合理假设下,通过定性分析宇宙尺度因子与参数之间的动态关系,发现宇宙的初始奇点是不可达的,K=1,0≤Λ<10-24ly-2 。这意味着,最初的大爆炸是不可能发生的,宇宙的空间结构应该是三维球面S3,宇宙的演化在时间上应该是循环的,宇宙学常数应为零或很小的量。由于证明过程是非常简单明确的,前提条件也都是公认的事实,因此这些逻辑结论应该是相当可靠的。显然,这些结论将有助于纠正一些流行的误解,并为进一步研究宇宙学中的其他问题如暗物质和暗能量的性质带来极大方便。从某种意义上讲,我们恢复了赫拉克利特的古老信念:“世界,这个万物的实体,既不是由神也不是由人创造的,她过去曾是、现在也是和将来还是永恒的活火,有规律地点燃并且有规律地熄灭”。

关键词: 宇宙模型,宇宙曲率;宇宙学常数;负压力;动态分析。

Abstract

In cosmology, the cosmic curvature K and the cosmological constant are two most important parameters, whose values have a strong influence on the behavior of the universe. Under the assumptions of positive energy density and negative initial pressure, by analyzing the dynamic relationship between cosmological variables and parameters, we find that the initial singularity of the universe is unreachable, and K=1,0≤Λ<10-24ly-2 . This means that the initial Big Bang may be impossible at all. The global spatial structure of the universe should be a 3-dimensional sphere S3 . The evolution of the universe should be cyclic, and the cosmological constant should be zero or an infinitesimal. Since the proof is very simple and elementary, and the preconditions are generally accepted facts, these logical conclusions should be quite reliable. Obviously such constraints would be much helpful to correct some popular misconceptions and further discover the properties of dark matter and dark energy in cosmology. In some sense, we restored Heraclitus' ancient faith: “The world, an entity out of everything, was created by neither gods nor men, but was, is and will be eternally living fire, regularly becoming ignited and regularly becoming extinguished.”

Key words: Cosmological Model; Cosmic Curvature; Cosmological Constant; Negative Pressure; Dynamic Analysis

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