Cosmic knots may finally explain why the Universe exists

A team of physicists in Japan has now shown that knotted structures can naturally appear in a realistic particle physics model that also addresses several major mysteries, including the origins of neutrino masses, dark matter, and the strong CP problem. Their study, published in Physical Review Letters, suggests that such "cosmic knots" could have formed in the violently changing early universe, briefly taken over as a dominant form of energy, and then collapsed in a way that slightly favored matter over antimatter. As they formed and decayed, these knots would have stirred spacetime itself, producing a distinctive pattern of gravitational waves that future detectors might be able to pick up, which is rare for a problem that is usually very difficult to test directly.

"This study addresses one of the most fundamental mysteries in physics: why our Universe is made of matter and not antimatter," said study corresponding author Muneto Nitta, professor (special appointment) at Hiroshima University's International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2) in Japan.

"This question is important because it touches directly on why stars, galaxies, and we ourselves exist at all."

The matter and antimatter imbalance

According to the Big Bang theory, the universe should have started with equal amounts of matter and antimatter. Each particle of matter has an antimatter partner with the same mass but opposite charge, and when they meet, they annihilate into pure energy. If everything had balanced perfectly, all matter and antimatter should have destroyed each other, leaving behind only radiation.

Instead, almost everything we observe today is made of matter, with almost no antimatter visible in the cosmos. Simple calculations show that the entire observable universe, from individual atoms to galaxy clusters, exists because, in the early universe, only one extra matter particle survived for every billion matter-antimatter pairs.

The Standard Model of particle physics, which successfully describes most known particles and forces, cannot explain this tiny but crucial asymmetry. Its predictions for the matter excess fall short by many orders of magnitude. Understanding how that small surplus of matter arose, a process known as baryogenesis, remains one of the central unsolved problems in physics.

Building a new model with cosmic knots

Nitta and Minoru Eto of Hiroshima University's WPI-SKCM2, a research center focused on knotted and chiral phenomena across different systems and scales, together with Yu Hamada of the Deutsches Elektronen-Synchrotron in Germany, argue that a plausible solution might be hiding in a well-motivated extension of known physics.

By combining a gauged Baryon Number Minus Lepton Number (B-L) symmetry with the Peccei-Quinn (PQ) symmetry, the team found that stable knotted configurations could naturally form in the early universe and later produce the observed matter surplus.

Eto is also a professor at Yamagata University, and all three scientists are affiliated with Keio University in Japan.

Ghostlike neutrinos, axions, and hidden symmetries

These two additional symmetries have been studied for decades because they help resolve some of the Standard Model's biggest shortcomings. The PQ symmetry addresses the strong CP problem, which asks why experiments fail to detect the tiny electric dipole moment that theory predicts for the neutron. In solving this puzzle, the PQ symmetry introduces the axion, a hypothetical particle that is a leading candidate for dark matter. At the same time, the B-L symmetry provides a natural explanation for why neutrinos have mass, even though they interact so weakly with matter that they can pass through entire planets without leaving a trace.

In this model, the PQ symmetry is kept as a global symmetry rather than being "gauged," which protects the delicate axion physics needed to solve the strong-CP problem. In physics, "gauging" a symmetry means allowing it to act independently at every point in spacetime. That kind of freedom comes at a price, because the theory then requires a new force-carrying particle to keep the equations consistent. By gauging the B-L symmetry instead, the researchers ensured the existence of heavy right-handed neutrinos, which are needed to cancel anomalies in the theory and play a key role in many baryogenesis scenarios. Gauging B-L also produces behavior similar to a superconductor and establishes the magnetic structure that allows some of the earliest knots in the universe to form.

Cosmic strings in the young universe

As the universe expanded and cooled after the Big Bang, it likely went through a series of phase transitions in which its symmetries broke down in stages. This process, which can be compared to water freezing into ice in an uneven way, may have left behind thin, thread-like defects known as cosmic strings. These objects are often described as cracks in spacetime and remain hypothetical, but many cosmologists consider them a serious possibility. Despite being thinner than a proton, just an inch of such a string could weigh as much as a mountain.

As the universe grew, a network of these strings would have stretched, twisted, and tangled, preserving information about the conditions that existed in the earliest moments.

The breaking of the B-L symmetry produced strings that behave like magnetic flux tubes, while the PQ symmetry created superfluid vortices that carry no magnetic flux. The stark difference between these two types of defects is exactly what allows them to fit together. The B-L flux tube provides a structure for the PQ superfluid vortex's Chern-Simons coupling to attach to. In turn, this coupling allows the PQ superfluid vortex to pump electric charge into the B-L flux tube and oppose the tension that would normally cause the loop to shrink and snap. The outcome is a long-lived, topologically locked state known as a knot soliton.

"Nobody had studied these two symmetries at the same time," Nitta said. "That was kind of lucky for us. Putting them together revealed a stable knot."

A knot-dominated era and quantum tunneling

Radiation in the expanding universe gradually lost energy as its wavelengths stretched with spacetime. The knots, however, behaved more like ordinary matter, so their energy density decreased much more slowly. As a result, they eventually came to dominate over radiation, creating a period in cosmic history in which the energy stored in knots controlled the evolution of the universe.

This phase did not last forever. The knots ultimately unraveled through quantum tunneling, a process in which particles cross energy barriers that would be insurmountable in classical physics, as if they were passing through a wall. When the knots collapsed, they produced heavy right-handed neutrinos as a direct consequence of the B-L symmetry embedded in their structure. These very massive, elusive particles then decayed into lighter, more stable particles with a slight preference for matter over antimatter. That tiny preference eventually led to the matter-filled universe we see today.

"Basically, this collapse produces a lot of particles, including the right-handed neutrinos, the scalar bosons, and the gauge boson, like a shower," study co-author Hamada explains. "Among them, the right-handed neutrinos are special because their decay can naturally generate the imbalance between matter and antimatter. These heavy neutrinos decay into lighter particles, such as electrons and photons, creating a secondary cascade that reheats the universe."

"In this sense," he added, "they are the parents of all matter in the universe today, including our own bodies, while the knots can be thought of as our grandparents."

Linking knot physics to today's universe

To test their idea, the researchers followed the mathematical consequences of their model in detail, including how efficiently the knots produce right-handed neutrinos, how heavy those neutrinos are, and how hot the universe becomes when they decay. From this calculation, the matter-antimatter imbalance observed today emerges naturally.

By rearranging the equations and assuming a realistic mass of 10¹² giga-electronvolts (GeV) for the heavy right-handed neutrinos, and that the knots transfer most of their stored energy into creating these particles, the model predicts a reheating temperature of about 100 GeV. This temperature happens to coincide with the last opportunity for the universe to generate matter from a neutrino imbalance. Below that temperature, electroweak processes that convert a neutrino asymmetry into an excess of matter effectively shut off.

Reheating to 100 GeV would also affect the universe's background of gravitational waves, shifting its spectrum toward higher frequencies. Future gravitational-wave observatories, including the Laser Interferometer Space Antenna (LISA) in Europe, Cosmic Explorer in the United States, and the Deci-hertz Interferometer Gravitational-wave Observatory (DECIGO) in Japan, may one day be able to detect this subtle change in the cosmic gravitational-wave signal.

"Cosmic strings are a kind of topological soliton, objects defined by quantities that stay the same no matter how much you twist or stretch them," Eto said. "That property not only ensures their stability, it also means our result isn't tied to the model's specifics. Even though the work is still theoretical, the underlying topology doesn't change, so we see this as an important step toward future developments."

From Kelvin's vision to a realistic knot model

Lord Kelvin originally suggested that knots might be the basic constituents of matter. That early idea turned out to be incorrect, but the new work brings back the spirit of his proposal in a more sophisticated way. The researchers argue that their results "provide, for the first time, a realistic particle physics model in which knots may play a crucial role in the origin of matter."

"The next step is to refine theoretical models and simulations to better predict the formation and decay of these knots, and to connect their signatures with observational signals," Nitta said. "In particular, upcoming gravitational-wave experiments such as LISA, Cosmic Explorer, and DECIGO will be able to test whether the Universe really passed through a knot-dominated era."

Ultimately, the team hopes to determine whether knotlike structures were truly essential in creating the matter in the universe. If so, they could help piece together a more complete and physically testable story of how the cosmos began.