de Sitter空间中光子及其玻色-爱因斯坦凝聚体暗能量的宇宙质量
Cosmological Mass of the Photon and Dark Energy as its Bose-Einstein Condensate in de Sitter Space
摘要：
基于量子力学（QM）和广义相对论（GR）的基本原理和常数，我发展了一个暗能量（DE）的物理图像。它来自一个猜想的非零质量的近标准模型的光子，基于量子局域化在宇宙学尺度。暗能量与德西特空间有关，并且具有基本不变的事件视界。我设想DE是宇宙学上大质量光子的玻色-爱因斯坦凝聚体（BEC），我从根本上估计了该BEC中有效吸引的QM势所产生的每个粒子的结合能。由于大量的光子可能会在一个平坦的空间几何的de Sitter宇宙中静止，我解决了时间无关的薛定谔方程的非相对论性吸引球势阱自约束在de Sitter视界。结合在该阱的顶部的粒子状态的最小临界势深度，结合标准平坦$Λ$-CDM模型中的暗能量-压力关系的原型条件，提供了光子质量$m_g$的估计。这是支持一个独立的计算的真空能量的BEC在德西特静态度规与坐标时间切片。这些估计提供了对暗能量凝聚的兼容解释，弥合了核尺度和宇宙尺度之间的鸿沟。最值得注意的是，我考虑了一个宇宙学单位系统，或称"$g$-单位"，它以各种方式补充了普朗克单位的基本系统。普朗克和$g$质量的几何平均值与目前中微子质量的估计值非常接近，这表明即使是已知最轻的费米子的质量也可能与GR和QM基本常数$Λ$、$G$、$c$和$h$密切相关。最后，我与精细结构常数$m_g$和库仑势限制在相应的宇宙视界。
英文摘要：
I develop a physical picture of dark energy (DE) based on fundamental principles and constants of quantum mechanics (QM) and general relativity (GR) theories. It derives from a conjecture of non-zero masses for nearly standard-model photons, based on QM localization at a cosmological scale. Dark energy is associated with de Sitter space and that has a fundamentally invariant event horizon. I conceive of DE as a Bose-Einstein condensate (BEC) of cosmologically massive photons and I estimate fundamentally the binding energy per particle originating from an effectively attractive QM potential in that BEC. Since massive photons may stand at rest in a de Sitter universe with flat spatial geometry, I solve the time-independent Schroedinger equation for a non-relativistic attractive spherical-well potential self-confining at the de Sitter horizon. The minimal critical potential depth that binds a particle state at the top of that well, combined with the prototypical condition of dark energy-pressure relation in the standard flat $Λ$-CDM model, provides an estimate of the photon mass, $m_g$. That is supported by an independent calculation of the vacuum energy of the BEC in a de Sitter static metric with coordinate-time slicing. These estimates provide compatible accounts of dark energy condensation, bridging a chasm between nuclear and cosmological scales. Most notably, I consider a system of cosmological units, or `$g$-units,' that complements the fundamental system of Planck units in various ways. The geometric mean of Planck and $g$-mass turns out to be remarkably close to current estimates of neutrino masses, suggesting that even masses of the lightest known fermions may be deeply related to both GR and QM fundamental constants $Λ$, $G$, $c$ and $h$. I finally relate the fine structure constant to $m_g$ and a Coulomb potential confined within a corresponding cosmological horizon.
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