Mohammed Guhdar
Researcher & Lecturer
College of Science, University of Zakho
Architect of Vacuum Fluid Theory (VFT): a quantitatively tested, hydrodynamic resolution to the dark-matter problem, built entirely within unmodified General Relativity.
mohammed.guhdar@uoz.edu.krd
What Vacuum Fluid Theory Is
The dark sector is not a gas of invisible particles (Cold Dark Matter) and not a modification of gravity (MOND). In VFT it is a real, continuous barotropic fluid that fills space, carries genuine thermodynamic pressure, condenses around ordinary matter, and settles into hydrostatic equilibrium — the same physics that shapes a star or a planetary atmosphere, applied to the dark sector.
The fluid has a sound speed $\sigma \approx 27$ km/s and an equation of state $P = \sigma^2 \rho$. Its outward pressure resists gravitational collapse, which is the physical reason galaxies have flat, cored centres instead of the sharp cusps that collisionless particles produce. Equilibrium is fixed by the Euler equation:
Because the sound speed is far below light speed, the relativistic weight of the pressure is negligible ($\sim 10^{-8}$), so gravity is left completely standard. Combining this balance with Poisson's equation yields the isothermal Lane–Emden equation; its non-singular solution (closely approximated by a pseudo-isothermal profile) guarantees the cored rotation curves seen in real galaxies.
The Three Pillars
The guiding aim: a dark sector that passes every test where CDM passes, and wins where CDM struggles — without abandoning General Relativity.
Galactic Kinematics — How It Is Tested
Every result below uses a strict fixed-baryon protocol — identical baryonic masses, optimiser, starting grid and weights for VFT, NFW and MOND — so no model is given a fitting advantage. The dataset is the public SPARC sample (165 galaxies fitted; 142 in the high-quality analysis set). VFT uses exactly two free parameters per galaxy ($V_\infty$, $r_s$); everything else is derived.
Rotation Curves
165 galaxies · fixed baryons · 2 paramsMedian fit quality R² = 0.961, ahead of NFW (0.924) and free-parameter MOND (0.791). The cored isothermal profile tracks the curves without modifying gravity.
Zero-Parameter RAR
Leave-one-out · global scaling relationsStripped of all per-galaxy parameters, VFT predicts the Radial Acceleration Relation with 0.193 dex scatter — matching parameter-free MOND (0.202 dex). Hydrostatic equilibrium plus population relations generates the RAR from photometry alone.
Baryonic Tully–Fisher
Independent photometric massesUsing light-based masses ($M_{\text{bar}} = 0.5L_{[3.6]} + 1.33M_{\text{HI}}$), VFT recovers the BTFR with correlation r = 0.939 and a slope bracketing the predicted $n = 4$.
Cored, Not Cusped
Analytic inner slopeThe fluid enforces a flat central core (inner density slope γ ≈ 0), replacing the steep cusp (γ ≈ −1) of collisionless dark matter — resolving the long-standing core–cusp problem.
Emergent Acceleration Scale
Derived, not assumedWith no acceleration scale built in, VFT produces one: $g_\dagger = V_\infty^2/r_s$, median 1.5 a₀. Unlike MOND's universal constant, VFT predicts a real ~0.4 dex galaxy-to-galaxy spread — a clean discriminator.
The Dual Signature
Adversarial CDM-mock controlOne equation predicts two opposite responses: hotter fluid expands the core, deeper baryonic potential compresses it (r = −0.576, p ≈ 10⁻¹⁴). The real SPARC signal exceeds the strongest signal any CDM mock could fake — a genuinely VFT-specific fingerprint.
Cosmological Validation — Planck & CLASS
To rival Cold Dark Matter, VFT must survive the early universe. Linear Einstein–Boltzmann runs with CLASS, evaluated against Planck high-$\ell$ data, show the phase-transitioning fluid is statistically indistinguishable from standard dark matter (Δχ² = +0.024) — clearing the barrier where modified-gravity theories have failed for forty years.
CMB Indistinguishability
CLASS · Planck plik-lite TTTEEEMatched-control runs give a mean spectral difference of only 2.8 × 10⁻⁵ from ΛCDM — invisible to the CMB while decisive inside galaxies.
The Phase Transition
First-law-preservingAt z_c ≈ 1240 the pressureless dark sector switches on pressure. Its Jeans mass there is ~10⁷ M☉, matching the scale of the first dwarf galaxies.
Particle Constraint
CLASS background tuningReproducing the condensation conditions points to a ~1.05 keV relic — VFT lands independently on the much-sought warm-dark-matter mass scale, but with pressure and cores that plain WDM lacks.
Lyman-α Resolved
Adiabatic cooling backgroundAs space expands the background fluid cools ($\sigma_{\text{bg}} \lesssim 5$ km/s), so its pressure cannot erase small-scale structure: 95.6% of power survives at $3\,h$/Mpc. The 27 km/s pressure is a property of collapsed halos, not the smooth background.
Cluster Mergers — The Superfluid Test
The hardest test for any fluid dark matter is the Bullet Cluster, where the dark matter passes straight through a collision and stays with the galaxies. A naive pressured fluid would shock and lag — the opposite. VFT confronts this directly with full smoothed-particle hydrodynamics (SPH) + N-body simulations.
Step 1 — The classical fluid honestly fails
Run as a plain pressured fluid, VFT's dark matter is dragged ~660 kpc behind its galaxies in a Bullet-speed collision, against a ~2 kpc collisionless baseline. This is exactly what the theory predicts a classical fluid should do — confirmed from inside the theory, not hidden.
Step 2 — The superfluid resolution
VFT's dark sector is a quantum condensate with a Landau critical velocity $v_c$. Collisions faster than $v_c$ break the condensate ($\sigma \to 0$, pressure vanishes) so the dark matter passes through like the Bullet; collisions slower than $v_c$ keep their pressure and drag, like the "train-wreck" cluster Abell 520. The discriminant is collision speed, not temperature. Tested with one fixed $v_c$, changing only the speed:
| Collision | Speed | Collisionless baseline | VFT superfluid offset | Behaviour |
|---|---|---|---|---|
| Fast (Bullet-like) | 4500 km/s > v_c | ~2 kpc | 19 kpc | passes through ✓ |
| Slow (Abell-like) | 2500 km/s < v_c | ~3 kpc | 874 kpc | drags ✓ |
Both halves of the prediction appear together with a single critical velocity, and the behaviour holds across a window of $v_c \approx 3000$–4000 km/s — not a fine-tuned value.
Step 3 — The hydrodynamics is validated
Because the whole result rests on the fluid shocking correctly, the same SPH engine was checked against the exact isothermal shock-tube solution. It reproduced the analytic answer to better than 1% on all three independent measures — shock position (0.8%), shocked density (0.1%) and velocity (0.3%) — with no spurious oscillations. The drag is real physics, not a numerical artifact.
Falsifiable Predictions
VFT is built to be broken if wrong. Its sharpest live tests:
JWST Core Evolution
Early dark-matter cores must follow $r_s \propto (1+z_{\text{form}})^{-3/2}$. The slope is fixed by the equation of state; JWST kinematics of ancient galaxies can confirm or kill it.
Acceleration-Scale Scatter
VFT requires the RAR transition to vary ~0.4 dex galaxy-to-galaxy; MOND forbids any scatter. Testable in existing data.
Small-Scale Power Cutoff
The cooling background imprints a WDM-like cutoff at $k_{1/2}\sim10$–30 $h$/Mpc — testable with satellite counts and strong-lensing substructure.
Merger Velocity Law
Merger drag should correlate with collision speed, not halo temperature — a critical $v_c$ separating Bullet-like pass-through from Abell-like drag across the observed cluster sample.
Interactive Dynamics: The VFT Simulation
To visualize how these physical principles govern the curvature of spacetime, an interactive VFT Simulation framework has been developed.
This computational tool allows researchers to actively adjust the fluid's thermodynamic sound speed and a galaxy's baryonic mass. By observing the resultant spacetime grid, users can visually analyze how hydrostatic equilibrium dictates galactic structure—transitioning smoothly from the dense gravity wells of cold halos to the broad profiles of hot, diffuse regimes.