Dark energy
One vacuum term
In v5.0 DFD has exactly one dark energy, the α⁵⁷ vacuum term. The dimming of distant supernovae is no longer read as an optical effect of the ψ field; that earlier reading, the ψ-screen, is retired.
A guide to Density Field Dynamics
Gravity is Light.
What if gravity isn’t curved spacetime, but a medium where light slows down near mass? This guide walks through the idea, the tests it has to pass, the numbers it claims to derive, and how it could be proven wrong. It takes about ten minutes.
Chapter one · The problem
Einstein was right. That’s the problem.
General Relativity has passed every test we have given it for more than a century. It explained Mercury’s orbit, predicted the bending of starlight, and forecast gravitational waves decades before anyone could detect them.
Yet when we use it to weigh the universe, the books don’t balance. The standard model of cosmology needs two ingredients that no one has ever seen directly.
- 1915Mercury’s odd orbit explained
- 1919Starlight bending measured during an eclipse
- 1971Clocks flown around the world tick differently
- 2015Gravitational waves detected
- 2019First image of a black hole
The universe’s missing 95%.
In the standard picture, ordinary matter makes up about 5% of the universe. That includes every star, planet, and person. The rest is dark matter and dark energy. Both are inferred from how things move, and neither has been detected in a laboratory.
- 5%Ordinary matter: stars, gas, planets, us
- 27%Dark matter, inferred from its pull
- 68%Dark energy, inferred from the dimming of distant supernovae
Galaxies spin too fast.
Stars far from a galaxy’s center should orbit slowly, the way the outer planets orbit the Sun slowly. They don’t. Measured speeds stay flat far past the point where the visible matter runs out.
Rotation curves of real galaxies
- Measured speed
- Newton, visible matter only
Real data from the SPARC catalogue (Lelli, McGaugh & Schombert 2016). The dashed line is what Newton’s law predicts from the stars and gas you can see. The standard fix is a halo of dark matter, fitted to each galaxy.
Chapter two · The theory
Space doesn’t curve. Light slows down.
Density Field Dynamics starts from a different picture. Space is flat, but it isn’t empty. It carries a field, ψ (psi), that grows near mass. Where ψ is larger, light travels more slowly, so its path bends, the way light bends through glass or shimmers over hot asphalt.
The same field tells matter how to fall. One field does the job that curved spacetime does in General Relativity.
n = eψ
The refractive index of space. Light’s local speed is c·e−ψ, so it slows and bends near mass.
a = ½c²∇ψ
The acceleration of a falling body. Matter slides down the slope of the same field.
Bend some light yourself.
Drag the mass
One switch between Newton and galaxies.
How strongly ψ responds depends on how strong gravity already is. DFD’s response function is μ(x) = x / (1 + x), where x compares the local acceleration with a tiny scale, a⋆ = 2√α·cH₀, about 1.2 × 10⁻¹⁰ m/s². Slide it and watch the two regimes.
78
Claims, each with a falsifier. The v5.0 release labels every claim by tier and lists every input of its graded predictions in one place: 45 validated, 8 pending, 23 open, 2 contested. The theory predicts, or it fails.
Galaxies, with nothing hidden.
Apply that one rule to the same galaxies, using only the stars and gas you can see. There is no dark matter halo and no galaxy-by-galaxy tuning. The same settings run for all five.
Rotation curves of real galaxies
- Measured speed
- Newton, visible matter only
- DFD μ-law, no dark matter halo
Same SPARC measurements. The gold line applies the μ-law with a⋆ = 2√α·cH₀ ≈ 1.2 × 10⁻¹⁰ m/s² and one fixed stellar mass-to-light ratio (0.5) for every galaxy. No halo is added.
Passing Einstein’s gauntlet.
Any rival to General Relativity has to match it wherever it has already been tested. In the weak-field limit DFD reproduces all ten post-Newtonian parameters, with γ = β = 1, so the classic tests come out the same.
Mercury’s orbit
Matches GRThe extra 43 arcseconds per century of perihelion shift.
Light deflection
Matches GRStarlight grazing the Sun bends by 1.75 arcseconds.
Shapiro delay
Matches GRRadio signals slow near the Sun by the amount Cassini measured.
Gravitational redshift
Matches GRClocks run slower deeper in a gravitational well, as GPS requires.
Gravitational waves
Matches GRThey travel at exactly c. In 2017 the gamma rays from a neutron-star merger arrived 1.7 seconds after its gravitational waves, after a 130-million-light-year trip.
Lunar laser ranging
Matches GRNo Nordtvedt effect: the Earth and the Moon fall toward the Sun alike.
Chapter three · The numbers
Where the constants come from.
The v5.0 framework goes further than gravity. It attaches a small internal space to every point, CP² × S³, seven extra dimensions curled up far below the reach of any microscope. The papers argue that this shape is the only one consistent with a few basic requirements on the vacuum, and that the forces and particles of the Standard Model follow from it.
The number 137.
The fine-structure constant, α, sets the strength of electromagnetism. Its inverse is about 137, and no accepted theory explains why. DFD’s v5.0 book gives a closed-form expression built from whole numbers that come from the internal geometry. It lands 4.9 parts per billion from the measured value. The step that ties one of its coefficients to electric charge is stated as not yet derived, so the book calls it a closed form rather than a derivation.
“One of the greatest damn mysteries of physics.”Richard Feynman, on the number 137
$$\alpha^{-1} = \frac{\pi^{3/2}}{24}\;\mathrm{Tr}(Y^2)\;k_{\max}\;\frac{k_{\max}+3}{k_{\max}+4}\;\left[1 + \frac{N_{\mathrm{sp}}}{g_F\;\mathrm{Tr}(Y^2)\;\bigl((k_{\max}+4)^2 - 1\bigr)}\right]$$
With Tr(Y²) = 10, kmax = 60, Nsp = 7, gF = 8.
137.?????????
Measured (CODATA 2022): 137.035999177
Press the button to compute DFD’s value.
Nine masses, one rule.
The same geometry sets the mass exponents of all nine charged fermions: the electron, muon, and tau, and the six quarks. The v5.0 release reports a 1.42% mean error at leading order across all nine. Seven of the prefactors are selected from data, and the book labels them that way.
- Quarks
- Charged leptons
Chapter four · The cosmos
A dark sector you can compute.
Standard cosmology treats dark matter and dark energy as ingredients whose amounts are measured, not explained. DFD’s v5.0 release derives the dark matter and traces the dark energy to a single vacuum term.
Dark matter
A derived particle, χ
32.005 eV
v5.0 derives a cold, collisionless component whose abundance, Ωχh² = 0.1193, is computed forward instead of fitted. That is 0.6σ from Planck, conditional on one identification of the field’s flux period. On the measured clock it reproduces the CMB third peak: H₃/H₂ = 0.977 and H₃/H₁ = 0.444, within 0.6σ.
The cosmological-constant problem
122.7 orders of magnitude
ρc/ρPl = (3/8π) C α⁵⁷
The largest mismatch in physics, between the vacuum energy theory expects and what we observe, appears in DFD as a power of α. The exponent is derived; the coefficient C in front of it is measured.
The Hubble tension
H₀ = 72.09 km/s/Mpc
Measurements of the expansion rate disagree: about 67 from the early universe and about 73 from nearby stars. DFD v5.0 reads both as right through one stated two-clock postulate. Clocks in bound matter give 72.09, close to the Cepheid-free local average of 71.87 ± 0.96. The early-universe clock reads H₀/λ, and a stated same-era rule predicts 67.79.
Standard cosmology
- Ordinary matter · about 5%
- Dark matter · about 27%, amount fitted to data
- Dark energy · about 68%, amount fitted to data
DFD v5.0
- Ordinary matter · unchanged
- Dark matter · the derived χ component, abundance computed
- Dark energy · one α⁵⁷ vacuum term, coefficient measured
Chapter five · The verdict
How to prove it wrong.
A theory is only as good as the experiments that could kill it. DFD’s predictions are frozen and dated. Here is where it is exposed.
Gravitational-wave speed
DFD requires gravitational waves to travel at exactly the speed of light.
DFD dies ifa difference is measured, even at one part in 10¹⁵.
The early expansion rate
DFD’s same-era rule predicts an early-universe Hubble rate of 67.79 km/s/Mpc.
DFD dies ifthe next DESI BAO release rules that value out.
Galaxies across cosmic time
DFD ties the galactic scale to the expansion rate, a⋆(z) = 2√α·cH(z), so it should have been larger in the early universe.
DFD dies ifa⋆ is found frozen at high redshift.
Precision clocks
In the core theory, clocks sitting side by side stay in step. The sharpest number is for the ²²⁹Th nuclear clock: a yearly modulation locked to perihelion, about 350 Hz half-amplitude in the extended theory and zero in minimal DFD.
DFD dies ifa Kennedy–Thorndike signal is seen, since the core theory predicts none.
Particle and survey experiments
v5.0 publishes frozen predictions, among them no proton decay, a spatially flat universe, and the CKM angle γ = 66.31°.
DFD dies ifresults land outside the stated ranges.
Checked so far.
γ = β = 1Matches every solar-system test of gravity
cT = cConsistent with the 2017 neutron-star merger
205 daysJILA’s silicon-cavity/Sr record supports the cavity–atom cancellation DFD derives
Every headline number in the v5.0 release can be rechecked. The book ships with its full LaTeX source, lists every input of its graded predictions in one appendix (App. FK), and labels each of its 78 claims by tier with a falsifier.
What if gravity really is light?
Einstein’s equations work. DFD asks whether the geometry behind them is the right picture, or a very good approximation of a simpler one. The experiments above will decide.
This guide summarizes Density Field Dynamics v5.0 (October 2026). All DFD papers are preprints.