Space as a Substance: A Glassy Vacuum

Space is treated as a single boundary-invariant quantum medium whose state of strain general relativity describes as geometry. Light and gravitational waves are its shear excitations, at one speed c = √(μ/ρ); its instantaneous elastic response is dark energy, with storage modulus K = ρ_Λc², and its slow relaxational response is the dark matter seen in galaxies. The medium is a chiral superfluid glass: a fermionic superfluid with internal orientation frozen in random directions, rigid enough to carry gravitational waves, able to twist and so carry light at the same speed, and frictionless to matter. The two-faces reading of the dark sector comes from superfluid-vacuum work and the elastic reading from solid inflation and elastic dark energy. The departure is twofold: the gravitational wave is the medium's own shear excitation, not a metric perturbation damped by a separate fluid, and causality ties the loss to the difference between fast and slow stiffness. By the Kramers–Kronig relation a vacuum with a relaxational response cannot be lossless, so gravitational waves damp over cosmological distances and the gravitational-wave luminosity distance exceeds the electromagnetic one, d_GW/d_EM > 1, rising with redshift against the exact lossless (geometric and superfluid) null. The magnitude is not fitted: a superfluid has no static shear stiffness, so all the glass's shear rigidity sits in its frozen texture and all of it relaxes, giving d_GW/d_EM = (1+z)^(ξ/2) with ξ = a₀/cH ≈ 0.2 the coefficient of the dark-sector acceleration scale, where viscous cosmologies carry a free viscosity. This single-relaxation law is achromatic, degenerate in form with the viscous-fluid offset; a broadband (constant-Q) loss would trend with frequency, but loss reaching observable frequencies would over-damp ground-based sources seen undamped, and with the Hubble frequency the one natural loss scale, every detector band lies in the achromatic wing. The distinctive content is a forbidden mismatch: one ξ sets both the offset, p = ξ/2 ≈ 0.1, and a₀ = ξcH, so the offset LISA standard sirens will measure to percent level must match the ξ from galactic rotation curves, or the single-medium reading fails. The medium set from a hot, flawless, shear-free melt in a first-order transition that does inflation's work: the melt's bulk sound, far faster than light, made the sky uniform before light cones existed, and because the melt carried no transverse waves the model predicts no primordial gravitational waves, r = 0, a test for coming B-mode surveys. Thermal fluctuations of the melt, frozen as scales leave its shrinking sound horizon, give the observed red tilt when the bulk sound falls as about the cube of the melt temperature, and their measured amplitude fixes the setting near 1.5–1.8 × 10¹⁰ GeV after eleven to twelve e-folds of supercooling, the walls carrying the released energy across cold bubble interiors and releasing it as heat where they collide; current gravitational-wave searches already hold the front to within about thirty times light speed when it set. Against the measured acoustic peaks the glass holds only if its dark-matter mass is carried by a cold condensate, a low note of the ringing the setting strikes, while its relaxation supplies the galactic acceleration scale. Open are what fixes ξ, which the deposited series measures but does not derive, and the melt-to-solid stiffness ratio.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-18
DOI
https://doi.org/10.5281/zenodo.23454717
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

Space as a Substance: A Glassy Vacuum

Nicholas Archer Sanders
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

Space as a Substance: A Glassy Vacuum

Nicholas Archer Sanders
preprint en

Abstract

Space is treated as a single boundary-invariant quantum medium whose state of strain general relativity describes as geometry. Light and gravitational waves are its shear excitations, at one speed c = √(μ/ρ); its instantaneous elastic response is dark energy, with storage modulus K = ρ_Λc², and its slow relaxational response is the dark matter seen in galaxies. The medium is a chiral superfluid glass: a fermionic superfluid with internal orientation frozen in random directions, rigid enough to carry gravitational waves, able to twist and so carry light at the same speed, and frictionless to matter. The two-faces reading of the dark sector comes from superfluid-vacuum work and the elastic reading from solid inflation and elastic dark energy. The departure is twofold: the gravitational wave is the medium's own shear excitation, not a metric perturbation damped by a separate fluid, and causality ties the loss to the difference between fast and slow stiffness. By the Kramers–Kronig relation a vacuum with a relaxational response cannot be lossless, so gravitational waves damp over cosmological distances and the gravitational-wave luminosity distance exceeds the electromagnetic one, d_GW/d_EM > 1, rising with redshift against the exact lossless (geometric and superfluid) null. The magnitude is not fitted: a superfluid has no static shear stiffness, so all the glass's shear rigidity sits in its frozen texture and all of it relaxes, giving d_GW/d_EM = (1+z)^(ξ/2) with ξ = a₀/cH ≈ 0.2 the coefficient of the dark-sector acceleration scale, where viscous cosmologies carry a free viscosity. This single-relaxation law is achromatic, degenerate in form with the viscous-fluid offset; a broadband (constant-Q) loss would trend with frequency, but loss reaching observable frequencies would over-damp ground-based sources seen undamped, and with the Hubble frequency the one natural loss scale, every detector band lies in the achromatic wing. The distinctive content is a forbidden mismatch: one ξ sets both the offset, p = ξ/2 ≈ 0.1, and a₀ = ξcH, so the offset LISA standard sirens will measure to percent level must match the ξ from galactic rotation curves, or the single-medium reading fails. The medium set from a hot, flawless, shear-free melt in a first-order transition that does inflation's work: the melt's bulk sound, far faster than light, made the sky uniform before light cones existed, and because the melt carried no transverse waves the model predicts no primordial gravitational waves, r = 0, a test for coming B-mode surveys. Thermal fluctuations of the melt, frozen as scales leave its shrinking sound horizon, give the observed red tilt when the bulk sound falls as about the cube of the melt temperature, and their measured amplitude fixes the setting near 1.5–1.8 × 10¹⁰ GeV after eleven to twelve e-folds of supercooling, the walls carrying the released energy across cold bubble interiors and releasing it as heat where they collide; current gravitational-wave searches already hold the front to within about thirty times light speed when it set. Against the measured acoustic peaks the glass holds only if its dark-matter mass is carried by a cold condensate, a low note of the ringing the setting strikes, while its relaxation supplies the galactic acceleration scale. Open are what fixes ξ, which the deposited series measures but does not derive, and the melt-to-solid stiffness ratio.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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