Published February 9, 2026 | Version v04.3
Preprint Open

Resolving the Hubble Tension through Vacuum Phase Transitions: An Entangled Substrate Model with Empirical Validation

Authors/Creators

  • 1. Independent Researcher

Description

Resolving the Hubble Tension through Vacuum Phase Transitions: An Entangled Substrate Model with Empirical Validation

PROJECT SUMMARY: THE UNIVERSE AS A SELF-REGULATING SUBSTRATE

THE CORE NARRATIVE

The Hubble Tension is cosmology's biggest current crisis: a >5 sigma disagreement on the universe's expansion rate (H0). Standard fixes add new particles or dark forces.

This work proposes the vacuum itself is an entangled substrate that changes properties with local environment — stiff superfluid at low accelerations (galactic/cosmic scales), liquid hydrodynamic at high accelerations (solar/local scales).

THE REGIME LENS

The H0 split is not error but physical refraction: early-universe data (CMB) passes through "stiff" vacuum (higher impedance → slower apparent expansion); late-universe data (SNe, Cepheids) through "liquid" phase (saturated → inflated local rate).

Like viewing through ice vs. water, the medium distorts observations differently.

MACHIAN AND SELF-REGULATING CORE

Gravity (G) is no isolated constant — it scales with expansion rate (G proportional to H), realizing Mach's Principle: local inertia emerges from the global cosmic state.

Expansion becomes a feedback loop between matter density and substrate impedance — no fine-tuned Dark Energy needed.

EMPIRICAL ANCHORS

SPARC galaxy rotation curves show distinct resonances in low- vs high-surface-density regimes (median lambda_res ≈ 2.47 kpc low-Sigma; scaling 5–9 kpc high-Sigma), proving phase-dependent vacuum behavior.

FALSIFIABILITY

Predicts JWST high-z (z=3, Cosmic Noon) resonances shrink to ~0.8 kpc. Confirmation would elevate this from hypothesis to paradigm-shifting theory.

KEYWORDS (enter separately in Zenodo field)

Hubble tension, vacuum hydrodynamics, modified gravity, galaxy resonances, cosmology, Mach's Principle, phase transitions, SPARC dataset.

Full methods, derivations, Python code (SPARC reanalysis + H(z) simulation), and reproducibility instructions in attached PDF and supplements.

Series information (English)

Danish Raza – Vacuum Substrate Series (Excerpts)

Compiled from provided drafts/preprints (January–February 2026). Equations rendered via MathJax.

Paper 3: The Impedance of Space: Emergent Galactic Dynamics and Baryonic Resonances from a Superfluid Vacuum

Author: Danish Raza (Independent Researcher)

Date: January 20, 2026

We propose that the physical vacuum is a relativistic superfluid described by a “Stiff” Equation of State (P = ρc²) and a conserved characteristic impedance of Z₀ ≈377 Ω. By applying the Principle of Least Action to this medium within the boundary conditions of the Hubble Radius (R_H), we provide a first-principles derivation of the MOND acceleration scale (a₀) and the critical baryonic surface density (Σ_ψ). Unlike phenomenological models, this framework uniquely predicts the emergence of a characteristic resonant scale for baryonic structures in the low-acceleration regime. We derive a “Vacuum Jeans Length”—defined by the impedance matching of baryonic thermal pressure to the vacuum acceleration limit—yielding a characteristic scale of λ ≈2.1 −2.5 kpc for typical galactic velocity dispersions. This theoretical prediction aligns with the median resonant wavelength of 2.47 kpc empirically detected in low-surface-density galaxies (Raza, 2025b). We establish the Vacuum Impedance framework as a falsifiable alternative to ΛCDM, uniquely predicting that the resonant length scales as λ_res ∝σ² and predicting specific cosmic variance in dynamic scales at high redshifts.

2 The Cosmological Derivation of Inertia (a₀)

We first establish the physical origin of the acceleration scale a₀. We postulate that the observable universe, defined by the Hubble Radius R_H, acts as a resonant cavity for inertial waves (Unruh radiation).

2.1 The Cosmic Cavity Resonance

For a standing wave to exist in a spherical manifold, its fundamental wavelength must match the circumference, not the radius. The boundary condition is:

\(\lambda_{\max} = 2\pi R_H\)

An object with acceleration a generates an inertial Unruh wave of length λ_U = c²/a. The minimum acceleration supported by the vacuum before the wave exceeds the cosmic horizon is:

\(a_0 = \frac{c^2}{\lambda_{\max}} = \frac{c^2}{2\pi R_H}\)

2.2 Numerical Validation

Using standard cosmological parameters (H₀ ≈70 km/s/Mpc, R_H ≈1.3 × 10^{26} m):

\(a_0 = \frac{(3 \times 10^8)^2}{2\pi (1.3 \times 10^{26})} \approx 1.1 - 1.2 \times 10^{-10} \, \mathrm{m/s^2}\)

This matches the empirical MOND acceleration scale derived from galactic rotation curves.

From this acceleration, we derive the critical surface density threshold using Gauss’s Law:

\(\Sigma_\psi = \frac{a_0}{2\pi G} \approx 0.286 \, \mathrm{kg/m^2}\)

3 The Scalar-Tensor Lagrangian

We formally describe the vacuum properties via a scalar-tensor field theory.

3.1 Physical Justification of Z₀

In Electromagnetism, Z₀ = √(μ₀/ε₀) ≈377 Ω represents the ratio of force-flux (E-field) to flow-potential (H-field). We argue that Z₀ is not merely an electromagnetic parameter, but a dimensional necessity for any medium that transmits stress-energy.

3.2 The Action

\(S = \int d^4x \sqrt{-g} \left[ \frac{R}{16\pi G} - \frac{(\partial\phi)^2}{2 Z_0} F\left(\frac{(\partial\phi)^2}{a_0^2}\right) + L_{\rm matter} \right]\)
 

Paper 4: The Impedance of Space II: Deriving Newtonian Gravity from Vacuum Hydrodynamics

Author: Danish Raza

Date: January 23, 2026

We present a derivation of Newtonian gravity and the Poisson equation from the properties of the physical vacuum, characterized by a fundamental impedance Z₀ ≈377 Ω. Building on the “Stiff” superfluid phase established in Papers 1–3, we demonstrate that in high-gradient stellar regimes, the vacuum undergoes a phase transition to a “Liquid” state. By modeling fundamental particles as topological defects (solitons) that act as sinks for vacuum energy, we derive the displacement field D directly from a conservation law analogous to Gauss’s Law. We show that Newton’s constant G is not fundamental, but is a composite parameter expressible in terms of the cosmological Hubble radius R_H and the baryonic surface-density threshold Σ_ψ. Furthermore, we derive the Schwarzschild metric’s optical path predictions by treating the vacuum density variation as a dielectric response, ensuring full consistency with Solar System relativistic tests. This framework unifies the thermodynamics of matter (from absolute zero to the Iron Peak) with the emergent geometry of spacetime.

2 Microphysics: The Atomic Churn

We model a baryon as a localized soliton or “Atomic Churn” that acts as a sink for vacuum energy. To maintain the soliton’s stability (the “crease”), there must be a continuous flux of vacuum displacement D directed inward. We postulate a conservation law for this vacuum flux, analogous to Gauss’s Law in electrostatics. For a particle of mass-energy mc²:

\(\oint \mathbf{D} \cdot d\mathbf{A} = -mc^2\)

Solving for a spherically symmetric point mass at radius r:

\(D(r) = -\frac{mc^2}{4\pi r^2} \hat{r}\)

3 Macrophysics: Deriving Newton’s Law

In the Liquid Phase (a ≫ a₀), the vacuum acts as a linear elastic medium. We posit a linear constitutive relation between the Vacuum Stress (Gravity g) and the Vacuum Strain (Displacement D).

\(g(r) \equiv 4\pi G_d \left( \frac{D(r)}{c^2} \right)\)

Substituting yields Newton’s inverse-square law:

\(g(r) = -\frac{G_d m}{r^2} \hat{r}\)

Identifying G_d ≡ G recovers Newton’s Law.

3.2 Unifying the Constants: The Relation of G to Hubble Radius and Density

\(G = \frac{c^2}{4\pi^2 R_H \Sigma_\psi}\)
 

Paper 3.5: The Entangled Substrate — Definitions, Regimes, and Consistency Requirements

Author: Danish Raza

Date: January 31, 2026

This paper (“Paper 3.5”) is an integrative overview of a research program that treats the physical vacuum as an active medium with characteristic constants (including the free-space impedance Z₀) and explores whether some large-scale gravitational regularities can be described as emergent, phase-dependent responses of this medium. Building on prior empirical analyses of disk galaxy rotation curves (Papers 1–2) and a proposed effective-field-theory formalism (Paper 3), we summarize two observationally motivated scales: a characteristic acceleration a₀ ∼10^{-10} m s^{-2} and a corresponding baryonic surface-density scale Σ_ψ = a₀/(2πG). We then outline how these scales enter a scalar-field “stiffness” framework and how, in the high-acceleration (Solar-System) limit, a vacuum-hydrodynamic construction can reproduce the Newtonian inverse-square law and the Poisson equation (Paper 4).

Table 1: Regime map used throughout the series.

Regime Diagnostic Effective description
Stiff / galactic a ≲ a₀ EFT stiffness (Paper 3)
Liquid / solar a ≫ a₀ Displacement hydrodynamics (Paper 4)
EM propagation J^μ = 0 Maxwell wave limit (required)
Entanglement claims spacelike separation No-signaling (required)

3 Consistency Requirements (Maxwell/Gravity/No-Signaling)

3.1 Electromagnetism: Maxwell limit

\(c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}\)

3.2 Gravity: Newtonian limit and weak-field tests

\(\nabla^2 \Phi = 4\pi G \rho\)

3.3 Entanglement: operational no-signaling

\(\sum_b P(a, b | x, y) = P(a | x)\)
 

Paper 2: Empirical Surface-Density–Dependent Resonances in Disk Galaxy Rotation Curves

Author: Danish Raza

Date: December 29, 2025

We report the reproducible empirical detection of baryonic surface-density–dependent resonant modes in disk-galaxy rotation curves using the open SPARC dataset (MassModels Lelli2016c.mrt, 171 galaxies). [...] Median wavelengths differ systematically between low- and high-density regimes, from 2.5 kpc in low-Σ systems to 5–9 kpc in high-Σ systems, with Kolmogorov–Smirnov p < 0.01 at all Σ_ψ. The analysis requires no fitted parameters and is entirely reproducible using public data and open Python code.

Σ_ψ (kg m^{-2}) N_low N_high λ̃_low (kpc) λ̃_high (kpc) KS p MW p
0.26 151 76 2.47 4.95 0.018 0.024
0.27 160 67 2.47 6.22 0.002 0.017
0.30 168 59 2.44 9.30 0.0003 0.002

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Additional details

Related works

Is supplement to
Dataset: 10.5281/zenodo.18035640 (DOI)
Dataset: 10.5281/zenodo.18110723 (DOI)
Preprint: 10.5281/zenodo.18319014 (DOI)
Preprint: 10.5281/zenodo.18457813 (DOI)
Preprint: 10.5281/zenodo.18354132 (DOI)

Software

Programming language
Python