Abstract
Abstract
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.