Where is dark matter hiding?
85% of the matter in the universe does not shine, does not reflect light, cannot be caught by our detectors. Yet it has mass — we see it spinning the galaxies. What if it were simply… too knotted?
Cosmology's quiet scandal
When astronomer Vera Rubin measured, in the 1970s, the rotation speed of stars in spiral galaxies, she found something absurd. According to Newton's laws (and Einstein's), stars far from the center should rotate more slowly, like planets far from the Sun. Instead they rotate just as fast as stars near the center.
The logical conclusion: galaxies contain far more mass than we can see. An invisible mass that holds the stars together by its gravity. This is dark matter.
Forty years of measurements have confirmed it: dark matter accounts for about 27% of the total energy of the universe, against only 5% for ordinary matter (your atoms, the stars, the visible galaxies). All the rest — 68% — is dark energy (the topic of the next lesson). In other words: we know what only 5% of the universe is made of.
Dark matter interacts gravitationally (we see it), but it does not interact with light — hence its name. It is also neutral with respect to the strong and weak nuclear forces: otherwise our detectors would already have caught it. How do you build a particle that interacts solely through gravity?
The dead end of classical candidates
For 40 years the physics community has searched for candidates: WIMPs, axions, sterile neutrinos, brown dwarfs, primordial black holes… All are add-ons to the Standard Model — one has to postulate a new particle with ad hoc properties that explain why we cannot see it.
The most sensitive experiments (XENON, LZ, ADMX) have been hunting these candidates for twenty years. The result: no detection. Each year the constraints tighten and rule out further chunks of parameter space. Many physicists are starting to wonder whether dark matter might be fundamentally different from what was imagined.
The TQNT idea: too knotted to shine
Back to Lesson 1: a particle is a knot. The more complex the knot, the heavier the particle. But — and this is the key point — the more complex the knot, the harder it becomes for it to interact with other particles.
Imagine two knots trying to exchange a photon. The photon must "couple" to both knots simultaneously. For simple knots (electron, quark) this is easy: their lobes are accessible. But for a very complex knot — say with 20 or 30 crossings — the lobes are tangled inside the knot itself, and the photon simply has no purchase.
TQNT even specifies the thresholds: beyond 18 crossings, the electromagnetic coupling collapses exponentially — each additional crossing divides it by 137. And the effective threshold of the dark reservoir, derived in V6, is 23 crossings: below it, a newborn knot stays coupled to the primordial plasma or does not survive; beyond it, it is dark and cosmologically eternal.
Dark matter would simply be matter that is too knotted. Beyond a certain threshold of topological complexity, a knot can no longer interact with photons, nor with the nuclear forces. Only its gravity remains. This is exactly what is observed for dark matter.
How many candidates?
How many different knots exist beyond these thresholds? Mathematicians have catalogued knots up to 30 crossings. The result: there are more than 1.5 million, and their number explodes exponentially with complexity. Applying its stability rules, TQNT finds there an immense reservoir of dark knots.
- 6 purely amphichiral knots — that is, identical to their mirror image, hence intrinsically neutral;
- 111 other knots whose charge can be neutralised by linking with other knots.
All share a common feature: they are absolutely stable. Their lifetime exceeds 10³⁴⁷ seconds (a number with 347 zeros). For comparison, the universe is 4 × 10¹⁷ seconds old. In short, once formed, these knots will never disappear.
Why 5.5 times more dark matter?
Cosmological measurements (notably from the Planck telescope) yield a precise ratio: there is 5.45 times more dark matter than ordinary matter in the universe. Where does this odd number come from? Why 5.45 and not 0.5 or 100?
TQNT answers: this ratio simply comes from the combinatorics of knots. During the Big Bang, all sorts of knots can form in the field. Simple knots (ordinary particles) are fewer than complex knots (dark matter), because there are more ways to tie something complicated than something simple.
The initial computation announced here “5.5, bullseye, with no adjustable parameter”. The audit refuted that fine number: the canonical reconstruction — parameter-free, from the surviving CP crumb on the visible side to the counting of freeze-out knots on the dark side — reaches the order of magnitude of the Planck measurement (5.45 ± 0.28), not the percent level. That is already remarkable: the ratio comes out of the mechanism, not out of a tuning. And the programme's register of honesty requires saying it that way.
Spherical halos, or why dark matter does not condense
A striking fact: dark matter does not form stars, nor planets, nor molecules. It remains dispersed in spherical halos around galaxies. Why?
TQNT's answer: no chemistry means no molecules. No molecules means no possible condensation. And no electromagnetism means no chemistry. Dark matter knots have no way to bind to one another except gravitationally — and gravity alone, at the particle scale, is far too weak to condense them. So they remain in a diffuse cloud, whose natural shape (under pure gravity) is a sphere.
This is exactly what astronomers observe. The spherical distribution of dark matter, often presented as a curiosity, becomes in TQNT a direct consequence of its lack of electromagnetism.
What if dark matter could clump together?
A recent paper ("Dark matter pearls", doi:10.5281/zenodo.20559267) explores a surprising variant: even without electromagnetism, dark matter could clump into invisible compact objects ranging from asteroid- to planet-sized, under the effect of topological Fermi pressure.
These "dark matter pearls" would weigh 10²⁰ to 10²⁷ kg — anywhere from a few lunar masses to a few planetary masses, compressed into a radius of 1 mm to 10 km. They would be detectable through:
- gravitational microlensing events with no luminous counterpart (Gaia, LSST, Roman);
- astrometric perturbations on nearby stars;
- possible mergers with neutron stars (LIGO).
If even one of these signatures is observed by 2030, it will be a strong argument in favour of TQNT. If none is, the "dark matter pearls" variant will be ruled out — but the spherical halo scenario remains valid. This is what is called a falsifiable prediction.
End-of-lesson quiz
Three questions to check your understanding.
1. According to TQNT, what characterises a dark matter knot?
2. Why does dark matter form spherical halos rather than stars?
3. Which TQNT prediction will we be able to test by 2030?