Dark energy
An optical effect
In DFD the dimming of distant supernovae comes from light crossing the ψ field on its way to us, which v4.0 calls a ψ-screen, rather than from a universe whose expansion is speeding up.
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.
0
Continuous fit parameters. The v4.0 release fixes its constants from theory instead of tuning them to data. 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 v4.0 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 v4.0 papers give a closed-form expression built from whole numbers that come from the internal geometry.
“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 is used to derive the masses of all nine charged fermions: the electron, muon, and tau, and the six quarks. The v4.0 release reports a 1.42% mean error across all nine, with no per-particle fitting.
- 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 v4.0 release tries to derive both.
Dark matter
A derived particle, χ
5.09 eV
v4.0 includes a cold, collisionless component whose abundance, Ωχh² = 0.1182, is computed forward from topology instead of fitted. Planck measures about 0.120.
The cosmological-constant problem
122.7 orders of magnitude
ρc/ρPl = (3/8π) α⁵⁷
The largest mismatch in physics, between the vacuum energy theory expects and what we observe, appears in DFD as a power of α, with no fine-tuning.
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’s v4.0 value is 72.09, within 0.3σ of the SH0ES and JWST measurements.
Standard cosmology
- Ordinary matter · about 5%
- Dark matter · about 27%, amount fitted to data
- Dark energy · about 68%, amount fitted to data
DFD v4.0
- Ordinary matter · unchanged
- Dark matter · the χ component, abundance computed
- Dark energy · replaced by an optical ψ-screen effect
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.
Black-hole shadows
DFD and General Relativity agree through second order and first differ at third. DFD predicts a shadow about 4.6% larger.
DFD dies ifnext-generation Event Horizon Telescope images match GR’s size.
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
Nuclear clocks built on ²²⁹Th, cross-species atomic comparisons, and cavity–atom tests probe how ψ couples to light and matter.
DFD dies ifthose comparisons show none of the channel-resolved signals it predicts.
Particle and survey experiments
v4.0 publishes frozen predictions for Belle II, JUNO, KATRIN, LISA, and Euclid.
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
Γ = 4Predicted for the solar corona; UVCS measured 4.4 ± 0.9
Every headline number in the v4.0 release can be rechecked. One command, python3 reproduce.py, recomputes them in about a minute and compares each with the value printed in the paper.
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 v4.0 (July 2026). All DFD papers are preprints.