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arXiv 0810.0752gr-qcastro-phcond-mat.stat-mech
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宇宙学常数的公理化方法

Axiomatic approach to the cosmological constant

Christian Beck

摘要:

关于宇宙学常数λ的理论目前还遥不可及。尽管如此,我们还是可以从一组公理开始,这些公理描述了一个宇宙学常数应该具有的最理想的性质。这可以从信息论中的欣钦公理(Khinchin axioms)的某些类比中看出,欣钦公理确定了信息度量应该具有的最理想的属性,并最终导致香农熵作为统计力学所基于的基本信息度量。在这里,我们制定了一套公理的宇宙学常数在密切类似的欣钦公理,正式取代的依赖关系的信息措施的事件概率的依赖关系的宇宙学常数的基本常数的性质。通过对这组公理进行评估,我们最终得到了一个宇宙学常数的公式,它由λ =(G^2/hbar ^4)(m_e/alpha_el)^6给出,其中G是引力常量,m_e是电子质量,alpha_el是精细结构常数的低能极限。该公式与当前WMAP数据完全一致。我们的方法给出了物理意义的爱丁顿-狄拉克大数假设,并建议观测值的宇宙学常数是不是在所有不自然的。

英文摘要:

A theory of the cosmological constant Lambda is currently out of reach. Still, one can start from a set of axioms that describe the most desirable properties a cosmological constant should have. This can be seen in certain analogy to the Khinchin axioms in information theory, which fix the most desirable properties an information measure should have and that ultimately lead to the Shannon entropy as the fundamental information measure on which statistical mechanics is based. Here we formulate a set of axioms for the cosmological constant in close analogy to the Khinchin axioms, formally replacing the dependency of the information measure on probabilities of events by a dependency of the cosmological constant on the fundamental constants of nature. Evaluating this set of axioms one finally arrives at a formula for the cosmological constant that is given by Lambda = (G^2/hbar^4) (m_e/alpha_el)^6, where G is the gravitational constant, m_e is the electron mass, and alpha_el is the low energy limit of the fine structure constant. This formula is in perfect agreement with current WMAP data. Our approach gives physical meaning to the Eddington-Dirac large number hypothesis and suggests that the observed value of the cosmological constant is not at all unnatural.

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