No dark matter particles · No free halo parameters · Only QCD + General Relativity
B. Kriger 2026
What is this? An interactive calculator that predicts galaxy rotation curves using only standard physics (QCD + General Relativity) — without dark matter particles. The αLGQV framework replaces the unknown dark matter halo with three known components: dead stars (from stellar evolution), CGM gas (observed by eROSITA), and excited quantum vacuum (from measured QCD sigma terms). The coupling constant α = 0.096 is measured, not fitted. Select any of the 20 galaxies below, or enter your own data.
Enter your own galaxy data. Paste radii and velocities as comma-separated values.
| Galaxy | Type | T | V_flat | R_d | f_dead | r_c | K_dead | K_rc | K_cgm | χ²_ν |
|---|
The vacuum of quantum chromodynamics (QCD) is the densest medium in the known universe. It is filled with the chiral condensate ⟨q̄q⟩ — a sea of virtual quark-antiquark pairs that spontaneously break chiral symmetry. This is not speculative: it is the foundation of hadron physics, confirmed by decades of experiment and lattice QCD calculations.
The energy density of the QCD condensate is enormous: ~10⁹ kg/m³ — comparable to a neutron star. Yet it does not gravitate in the standard model because of an assumed (but never proven) exact cancellation. In αLGQV, we do not assume this cancellation. Instead, we observe that the condensate shifts in the presence of baryonic matter, and this shift gravitates.
The proton mass is 938 MeV. But the Higgs mechanism gives its three valence quarks only ~9 MeV (~1%). The remaining 99% comes from QCD fields: gluons, virtual pairs, and the chiral condensate.
The proton's color field displaces the condensate around it. This displacement is measured by the sigma terms:
The strangeness sigma term σs is particularly revealing: the proton contains no strange valence quarks, yet σs ≠ 0. This means the proton modifies the vacuum s̄s fluctuations around it. This is direct, model-independent evidence that baryons modify the vacuum energy.
The total vacuum energy shift per nucleon:
Each nucleon carries ~10% of its mass as shifted chiral condensate with equation of state w = −1 (Lorentz scalar). This is the same equation of state as dark energy — because it is the same physics, just local instead of cosmological.
Every fermion in interstellar space excites the vacuum through three mechanisms at once (Paper #4, Section 2 of Volume I):
Vacuum energy = sum of zero-point energies of all field modes. A real fermion occupies a quantum state → that mode is blocked. The vacuum with fermions is a different state than without. Suppression ∝ fermion density.
Every electron, every quark in CGM does this.
Every charge polarizes the vacuum — virtual e⁺e⁻ pairs orient in the field. Polarized vacuum ≠ unpolarized vacuum energetically. Confirmed: Lamb shift, muon g−2, ATLAS light-by-light (2017).
Every charged particle in the galaxy does this.
Mass curves spacetime. Curved spacetime modifies the vacuum mode spectrum (Birrell & Davies 1982). Different boundary conditions → different zero-point energy. Same physics as the Casimir effect, but gravitational.
The entire gravitational well does this.
All three act in the same direction: matter suppresses vacuum energy locally. On cosmological scales, they combine into a single effective coupling:
Inside a star, nucleons are packed at high density. Nonlinear self-screening (Paper #9) reduces the effective coupling: αscr ≈ 0.005.
A lone proton in the CGM — surrounded by vacuum — uses the full bare coupling: αbare ≈ 0.096. No screening. Each of ~10⁶⁸ protons in the CGM independently excites the vacuum around it.
The QCD condensate energy density is ~10⁹ kg/m³. The needed vacuum excitation for flat rotation curves is ~10⁻²⁵ kg/m³. This is a fraction of 10⁻³⁴ of the condensate — an absolutely negligible perturbation. Like a ripple of 10⁻³⁴ on the surface of an ocean.
The gravitational well of the galaxy (Φ/c² ~ 10⁻⁷) easily produces this. The question is not "is there enough energy?" — the question is "what controls the tap?" The answer: the screening factor, which is the same physics as the cosmological constant problem.
R — Einstein gravity. R²/(6M²) — spacetime elasticity (Starobinsky). (1+2α)ℒm — vacuum-matter coupling. Three terms, one action, zero new particles.
v²bar(r) = Υd·V²disk + Υb·V²bul + |Vgas|·Vgas
Vdisk, Vbul, Vgas — from SPARC Table 2 (3.6 μm photometry + 21 cm HI). OBSERVED
Υd = 0.5 M☉/L☉ — disk mass-to-light ratio at 3.6 μm. STANDARD
fdead — ratio of dead stars to living stars, from population synthesis. Only 15% remain in the thin disk; the rest contribute through the vacuum halo. CALCULATED
(1+2αscr) = 1.01 — effective gravitational coupling inside stars (screened). DERIVED
Gas surrounding the galaxy out to 200–300 kpc. Primordial gas that never fell into the disk (angular momentum) + gas ejected by galactic winds (supernovae, AGN).
MCGM = 0.75·fb·Mhalo·Kcgm
β-model profile: ρ(r) ∝ [1+(r/rcore)²]−3β/2, β ≈ 0.5
Normalization: from eROSITA X-ray observations (Zhang+2024): 0.8–3.5 × 10¹¹ M☉ for MW-mass galaxies. OBSERVED
(1+2αbare) = 1.19 — unshielded protons in CGM use the bare coupling. MEASURED
The gravitational potential well of the galaxy excites the QCD chiral condensate. This excitation is self-gravitating and settles into an isothermal sphere:
ρvac(r) = ρ0 / [1 + (r/rc)²]
v²vac(r) = 4πGρ0r²c·[1 − (rc/r)·arctan(r/rc)]
rc = Krc·Rd — vacuum core radius equals the disk scale length, modified by galaxy morphology. DERIVED
ρ0 — determined self-consistently: the potential well depth sets how much vacuum is excited. Not fitted — follows from the baryonic distribution. SELF-CONSISTENT
The single fundamental parameter of αLGQV:
σπN = 59 MeV — pion-nucleon sigma term. Measures how much the proton mass comes from the chiral condensate. From πN scattering data + lattice QCD. MEASURED
σs = 40 MeV — strangeness sigma term. The proton has no strange valence quarks, but σs ≠ 0 because the proton modifies the vacuum s̄s fluctuations around it. This proves that baryons modify the vacuum energy. MEASURED
Screening: Inside stars, nonlinear self-screening (Paper #9) reduces αbare → αscr ≈ 0.005. In the diffuse CGM, each proton is isolated — full αbare ≈ 0.1 applies.
Galaxy shape (Hubble type T) determines the star formation history, wind efficiency, and potential well depth. Three coefficients modify the base formula:
| T | Type | Kdead | Krc | Kcgm | Physics |
|---|---|---|---|---|---|
| −5 | E | 1.50 | 0.50 | 1.50 | Old, deep well, hot X-ray halo |
| 0 | S0 | 1.40 | 0.60 | 1.40 | Lenticular, little gas |
| 3 | Sb | 1.13 | 0.87 | 1.13 | Classical spiral, large bulge |
| 5 | Sc | 1.00 | 1.00 | 1.00 | Standard (NGC 3198) |
| 8 | Sdm | 1.30 | 1.50 | 0.80 | Late-type, low-Z → top-heavy IMF longer |
| 10 | Im | 0.70 | 2.00 | 0.60 | Dwarf, shallow well → extended core |
Krc solves the cusp-core problem automatically: dwarfs (T=10) have Krc=2.0 → large vacuum core → flat center (core). Ellipticals (T=−5) have Krc=0.5 → compact core → steep rise. Not fitted — consequence of potential well depth.
2 free halo parameters per galaxy (ρs, rs)
Unknown particle — 40 years of searches, zero detections
LUX, XENON, PandaX, LHC, ADMX — nothing found
Can fit anything → cannot be falsified by rotation curves
Zero free halo parameters
α = 0.096 from QCD σ-terms — already measured
Uses only: protons, neutrons, photons, GR
Dead stars + CGM gas + vacuum excitation = rotation curves
Theory: Kriger B. 2026, "A Dark-Sector-Free Cosmology" Volumes I & II
σ-terms: Hoferichter M. et al. 2015, PRL 115, 092301; Alarcón J.M. et al. 2021, PRL 127, 092001
SPARC data: Lelli F., McGaugh S., Schombert J. 2016, AJ 152, 157
CGM mass: Zhang Y. et al. 2024, A&A (eROSITA); Tumlinson J. et al. 2017, ARA&A 55, 389
Winds: Heckman T. & Thompson T. 2017, arXiv:1701.09062; Muratov A. et al. 2015, MNRAS 454, 2691
Magnetic fields: Beck R. 2015, A&A Rev 24, 4
Vacuum QFT: Birrell N.D. & Davies P.C.W. 1982, "Quantum Fields in Curved Space"