Quantum ‘Knots’ Theory Could Explain Why Matter Exists

The universe’s first moments after the Big Bang were strange beyond imagination. Now physicists have discovered they may have been even weirder than we thought, dominated by enormous, twisted knots of energy that eventually collapsed to create all the matter around us.

When two fundamentally different types of cosmic strings link together, they form stable knots that physics won’t allow to untangle. These knotted structures could have briefly outweighed everything else in the cosmos, and their decay might finally explain one of science’s biggest mysteries: why matter exists at all.

Physicists from Japan and Germany have shown for the first time that these knot structures emerge naturally in realistic particle physics models. Published in Physical Review Letters, the work demonstrates how linking two distinct types of stringlike defects creates something entirely new: topologically stable solitons that trap energy in twisted configurations.

Until now, no one had proven that knots could appear in the models physicists actually use to explain real-world phenomena. That’s changed.

What Happens When Cosmic Strings Link Together

Cosmic strings are thin tubes of concentrated energy that formed when the universe cooled after the Big Bang. Think of cracks appearing in ice as water freezes. But unlike cracks, these cosmic defects come in fundamentally different varieties.

One type, called a flux tube, carries a magnetic field and behaves like a superconductor. Another type, a superfluid vortex, contains no magnetic field and acts more like a cosmic whirlpool. On their own, loops of either type would normally shrink and disappear due to their tension, like contracting rubber bands.

Linking changes everything. When a loop of one string type threads through loops of the other type, a quantum effect called the Chern-Simons coupling kicks in. This interaction gives the flux tubes an electric charge proportional to how many times the strings wrap around each other, a quantity mathematicians call the linking number.

That electric charge prevents the linked loops from collapsing. Flux tubes can’t shrink because they’re now electrically charged, and they can’t unlink because the strings repel each other when they try to pass through one another. What emerges is a stable knot that can persist indefinitely.

Computer simulations confirmed the effect. Visualizations show string loops braided together in space, with magnetic fields streaming along the flux tubes and electric fields radiating outward from their charged surfaces.

When Knots Ruled the Universe

If cosmic strings formed in the early universe at the right temperature, some would have randomly linked together, creating these stable knots throughout space. Most strings organized into sprawling networks, but the linked loops froze into their knotted configurations.

As the universe expanded, radiation thinned out while the knot density stayed constant. Eventually, the knots contained more energy than all the radiation in the cosmos combined. Researchers call this period the “knot dominated era.”

This epoch lasted until quantum mechanics intervened. Even though the knots are classically stable—meaning ordinary physics can’t break them—they can decay through quantum tunneling, where they essentially slip through energy barriers that would otherwise keep them intact. When the knots collapsed, they released their energy back into lighter particles, reheating the universe before Big Bang nucleosynthesis began forging the first atomic nuclei.

The timing is critical. For the universe to produce the elements we observe today, this reheating had to occur at temperatures above roughly 1 million electron volts. Knot decay naturally satisfies this requirement while opening a window to explain another cosmic mystery.

Why Matter Survived and Antimatter Didn’t

Collapsing knots offer a potential solution to one of physics’ biggest puzzles: why the universe contains matter but almost no antimatter. When particles meet their antimatter counterparts, they annihilate in bursts of energy. Yet somehow, a tiny excess of matter survived to form everything around us.

Decaying knots could produce right-handed neutrinos, which are exotic particles that couple to regular matter through specialized interactions. When these neutrinos decay, they can violate certain symmetries in ways that favor matter over antimatter.

The calculations show that knot decay could generate exactly the matter-antimatter imbalance observed today if the reheating temperature after knot collapse exceeds 100 billion electron volts. At that temperature scale, the processes that convert lepton asymmetry into baryon asymmetry remain active.

How much energy from each decaying knot goes into producing the lightest right-handed neutrinos determines the final outcome. When that fraction reaches reasonable values and the neutrino mass sits around 1 trillion electron volts, the observed matter-antimatter ratio falls out naturally. Alternative scenarios exist even if the reheating temperature drops below the critical threshold, giving the theory flexibility.

How We’ll Know If This Actually Happened

Networks of cosmic strings produce gravitational waves, and a knot-dominated era would leave distinctive fingerprints in the gravitational wave spectrum. Future detectors including the Cosmic Explorer and LISA will be sensitive enough to spot these signals.

Current gravitational wave data from NANOGrav have already detected possible signals from cosmic strings. Models show how the spectrum would deviate from the conventional prediction if a knot-dominated era occurred. Cosmic Explorer should be able to distinguish between these scenarios within the next decade.

Researchers calculated the expected gravitational wave spectrum for three different reheating temperatures: 5 million electron volts, 100 billion electron volts, and 100 trillion electron volts. Each produces a distinct deviation from the standard prediction. The 100 billion electron volt scenario—which matches the requirements for matter generation—falls squarely in the detection range of upcoming experiments.

If future gravitational wave detectors fail to observe these deviations, the knot domination theory would face serious constraints. The researchers note that few other cosmological scenarios involving matter generation offer such clear observational tests.

The Bigger Picture

Beyond the knot physics itself, this work connects to well-motivated extensions of the Standard Model. One symmetry in the model corresponds to the Peccei-Quinn symmetry, which solves the strong CP problem and predicts the QCD axion, a leading dark matter candidate. Another symmetry corresponds to B-L (baryon number minus lepton number), which explains tiny neutrino masses through what physicists call the seesaw mechanism.

Both symmetries were already favored for independent reasons. Combining them doesn’t introduce new puzzles, and their spontaneous breaking at similar energy scales fits naturally into frameworks like grand unified theories.

Making the knots stable requires specific conditions. One coupling constant must be roughly 1,000 times larger than another to prevent the strings from passing through each other and unlinking. A parameter governing the Chern-Simons interaction needs to reach values around 400 to generate enough electric charge to stabilize the configurations.

These requirements are demanding but not impossible. Quantum corrections from matter particles can naturally generate the Chern-Simons coupling at the required strength through loop effects involving fermions charged under both symmetries. However, whether this occurs in actual physical systems remains to be verified through more detailed calculations.

Lord Kelvin’s 19th-century hypothesis that atoms were knots in the aether turned out to be wrong, but it sparked the development of knot theory in mathematics. More than a century later, knots have found their way back into fundamental physics through this realistic particle theory. The knotted strings aren’t atoms, but they may have played a crucial role in creating the matter that eventually formed atoms, stars, and galaxies.