Knots today arise in various fields of mathematics and physics. A team of physicists from Japan and Germany suggests that the early Universe may have experienced a “node-dominated era” when nodes were the dominant component of the Universe, a scenario that can be tested using observations of gravitational waves; Moreover, they suggest that the end of this era will involve the collapse of nodes through quantum tunneling, leading to the formation matter-antimatter asymmetry in the Universe.
The model proposed by This etc.. suggests a short, node-dominated epoch where these entangled energy fields outweighed everything else, a scenario that could be probed using gravitational wave signals. Image credit: Muneto Nitta/Hiroshima University.
Knots, mathematically defined as closed curves embedded in three-dimensional space, appear today not only in tying a tie, but also in various scientific fields. Lord Kelvin.
Although his hypothesis that atoms were knots of ethereal vortices was eventually disproved, it stimulated the development of knot theory and its applications in many areas of physics.
“Our research addresses one of the most fundamental mysteries in physics: why our universe is made of matter and not antimatter,” said Professor Muneto Nitta, a physicist at Hiroshima University and Keio University.
“This question is important because it directly affects the question of why stars, galaxies, and ourselves exist at all.”
“The big bang would have produced equal amounts of matter and antimatter, each particle destroying its twin until all that was left was radiation.”
“However, the universe is overwhelmingly composed of matter, with almost no antimatter observed.”
“Calculations show that everything we see today, from atoms to galaxies, exists because for every billion matter-antimatter pairs, only one extra particle of matter survived.”
“The Standard Model of particle physics, despite its extraordinary success, cannot explain this discrepancy.”
“His predictions are off by many orders of magnitude.”
“Explaining the origin of this tiny excess of matter, known as baryogenesis, is one of the greatest unsolved mysteries in physics.”
By combining baryon number minus lepton number (BL) gauge symmetry with Peccei-Quinn (PQ) symmetry, Professor Nitta and his colleagues showed that knots could form naturally in the early Universe and generate the observed excess.
These two long-studied extensions of the Standard Model address some of its more puzzling gaps.
PQ symmetry solves the strong CP problem, the puzzle of why experiments fail to detect the tiny electric dipole moment that theory predicts for the neutron, and in the process introduces the axion, a leading candidate for dark matter.
Meanwhile, BL symmetry explains why neutrinos, ghostly particles that can slip through entire planets unnoticed, have mass.
Preserving PQ symmetry global, rather than measuring it, preserves the subtle axion physics that solves the strong CP problem.
In physics, “valuing” symmetry means allowing it to act freely at every point in spacetime.
But this local freedom comes at a price. To maintain consistency, Nature must introduce a new force to smooth out the equations.
By measuring BL symmetry, the researchers not only guaranteed the presence of heavy right-handed neutrinos (which is necessary for the theory to be free of anomalies and central to leading models of baryogenesis), but also introduced superconducting behavior that provided the magnetic basis for perhaps some of the earliest knots in the Universe.
As the universe cooled after the Big Bang, its symmetry broke through a series of phase transitions and, like the uneven freezing of ice, may have left behind thread-like defects called cosmic strings, hypothetical cracks in spacetime that many cosmologists believe may still exist.
Although a string is thinner than a proton, an inch of string can outweigh mountains.
As the cosmos expanded, the twisting web of these threads stretched and tangled, bearing within them the imprints of the primordial conditions that once prevailed.
The breaking of BL symmetry led to the formation of flux tube strings, and the PQ symmetry led to the appearance of superfluid vortices without flow.
It is their contrast that makes them compatible.
The BL flow tube gives the Chern-Simons coupling of the PQ superfluid vortex something to grab onto.
And in turn, the coupling allows the superfluid vortex pump PQ to charge into the flux tube BL, counteracting the stress that would normally cause the loop to break.
The result is a metastable, topologically blocked configuration called a nodal soliton.
“No one has studied these two symmetries simultaneously,” said Professor Nitta.
“It was kind of a stroke of luck for us. By putting them together, we had a stable unit.”
While the radiation lost energy as its waves stretched out through spacetime, the nodes behaved like matter, decaying much more slowly.
They soon overtook everything else, ushering in an era of node dominance, when their energy density rather than radiation ruled the cosmos.
But this reign did not last long. The knots were eventually untangled thanks to quantum tunneling, a ghostly process in which particles slip through energy barriers as if they were not there at all.
Their collapse produced heavy right-handed neutrinos, a built-in consequence of the BL symmetry woven into their structure.
These massive ghostly particles then decayed into lighter, more stable forms with a slight bias toward matter rather than antimatter, giving us the Universe we know today.
“Essentially, this collapse produces a variety of particles, including right-handed neutrinos, scalar bosons and a gauge boson, like rain,” said Dr Yu Hamada, a physicist at the German Electron Synchrotron and Keio University.
“Among them, right-handed neutrinos are special because their decay can naturally cause an 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, they are the parents of all matter in the universe today, including our own bodies, and the nodes can be considered our grandparents.”
When the researchers followed the mathematics built into their model (how efficiently the nodes produced right-handed neutrinos, how massive those neutrinos were, and how hot the cosmos was after they decayed), the matter-antimatter imbalance we see today naturally emerged from the equation.
If we change the formula and introduce a realistic mass of 1012 gigaelectronvolts (GeV) for heavy right-handed neutrinos, and assume that the nodes devoted most of their stored energy to creating these particles, the model would naturally land at a reheat temperature of 100 GeV.
This temperature coincidentally marks the last window in the universe for the creation of matter.
If it gets colder, the electroweak reactions that convert the imbalance of neutrinos into matter will stop forever.
Reheating to 100 GeV would also change the chorus of gravitational waves in the universe, shifting it toward higher frequencies.
Future observatories such as the Laser Interferometer Space Antenna (LISA) in Europe, Cosmic Explorer in the US, and the Decihertz Interferometer Gravitational-Wave Observatory (DECIGO) in Japan will one day be able to hear this subtle change in tuning.
“Cosmic strings are a kind of topological soliton, objects defined by quantities that remain the same no matter how much you twist or stretch them,” said Dr. Minoru Eto, a physicist at Yamagata University, Keio University and Hiroshima University.
“This property not only ensures their stability, but also means that our result is not tied to the features of the model.”
“Even though the work is still theoretical, the underlying topology does not change, so we see this as an important step towards future developments.”
Lord Kelvin originally suggested that knots were the fundamental building blocks of matter, but the researchers say their findings provide the first realistic model of particle physics in which knots may play a crucial role in the origin of matter.
“The next step is to improve theoretical models and simulations to better predict the formation and decay of these nodes, and to relate their signatures to observational signals,” Professor Nitta said.
“In particular, upcoming gravitational wave experiments such as LISA, Cosmic Explorer and DECIGO will be able to test whether the Universe has indeed experienced a knot-dominated era.”
teams Job appears in the magazine Physical Review Letters.
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Minoru This etc.. 2025. Tying Knots in Particle Physics. Phys. Reverend Lett 135, 091603; doi: 10.1103/s3vd-brsn
