It is well known that the cosmological constant term in the Einstein field equations can be interpreted as a stress tensor for dark energy. This stress tensor is formally analogous to an elastic constitutive equation in continuum mechanics. As a result, the cosmological constant leads to a “shear modulus” and “bulk modulus” affecting all gravitational fields in the universe. The form of the constitutive equation is also analogous to the London constitutive equation for a superconductor. Treating dark energy as a type of superconducting medium for gravitational waves leads to a Yukawa-like gravitational potential and a massive graviton within standard General Relativity. We discuss a number of resulting phenomenological aspects such as a screening length scale that can also be used to describe the effects generally attributed to dark matter. In addition, we find a gravitational wave plasma frequency, index of refraction, and impedance. The expansion of the universe is interpreted as a Meissner-like effect as dark energy causes an outward “expulsion” of space-time similar to a superconductor expelling a magnetic field. The fundamental cause of these effects is interpreted as a type of spontaneous symmetry breaking of a scalar field. There is an associated chemical potential, critical temperature, and an Unruh-Hawking effect associated with the formulation.

中文翻译：

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暗能量作为超导介质的引力子质量——理论和现象学方面


众所周知，爱因斯坦场方程中的宇宙常数项可以解释为暗能量的应力张量。该应力张量在形式上类似于连续介质力学中的弹性本构方程。因此，宇宙学常数导致影响宇宙中所有引力场的“剪切模量”和“体积模量”。本构方程的形式也类似于超导体的伦敦本构方程。将暗能量视为引力波的一种超导介质，会产生标准广义相对论中的汤川引力势和大质量引力子。我们讨论了许多由此产生的现象学方面，例如也可用于描述通常归因于暗物质的影响的筛选长度尺度。此外，我们还发现了引力波等离子体频率、折射率和阻抗。宇宙的膨胀被解释为类似迈斯纳效应，因为暗能量导致时空向外“排斥”，类似于超导体排斥磁场。这些效应的根本原因被解释为标量场的一种自发对称性破缺。配方中存在相关的化学势、临界温度和安鲁-霍金效应。