In 1867, Lord Kelvin famously envisioned atoms as knots tied in the fabric of the aether, a concept that was ultimately dismissed as atomic theory evolved. Yet, this long-abandoned idea might hold profound implications for our understanding of the universe’s origin and the fundamental asymmetry between matter and antimatter. Recent breakthroughs by Japanese physicists have resurrected Kelvin’s knot concept, not as a mere curiosity, but as a cornerstone in a sophisticated particle physics framework addressing some of the most pressing mysteries in contemporary science—namely neutrino masses, dark matter, and the baryon asymmetry of the universe.
For the first time, researchers at Hiroshima University’s International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM²), led by Professor Muneto Nitta, alongside collaborators at Keio University and Deutsches Elektronen-Synchrotron in Germany, have demonstrated that topologically knotted field configurations can naturally arise during the early, turbulent moments following the Big Bang. Their study, recently published in Physical Review Letters, suggests these “cosmic knots” may have briefly dominated the primordial cosmos, undergoing collapse processes that favored the production of matter over antimatter—a phenomenon elusive to observation but potentially traceable via gravitational wave signatures detectable by upcoming observatories.
The intellectual quandary tackled by this work is known as baryogenesis—the puzzle that, according to the Standard Model of particle physics, the Big Bang should have created matter and antimatter in equal quantities. Given that matter and antimatter annihilate upon contact, the universe should have been left flat, populated solely by radiation. Contrary to this, a slight preponderance of matter survived, one particle per billion matter-antimatter pairs, giving rise to everything we observe today. This scarcity defies Standard Model predictions, which underestimate the asymmetry’s magnitude by several orders of magnitude, compelling physicists to search beyond classical paradigms for viable mechanisms.
The team’s innovative approach synthesizes two pivotal symmetries beyond the Standard Model: the gauged Baryon Number Minus Lepton Number (B−L) symmetry and the global Peccei–Quinn (PQ) symmetry. Each addresses longstanding theoretical challenges. The B−L symmetry furnishes a natural explanation for neutrino masses via the inclusion of heavy right-handed neutrinos, while the PQ symmetry, introduced to solve the strong CP problem, predicts the axion, an eminent dark matter candidate. By gauging the B−L symmetry and preserving the global PQ symmetry, the researchers uncovered a fertile ground for topological constructs to emerge, bringing together magnetic flux tubes and superfluid vortices into energetically stable, knotted configurations known as knot solitons.
These knot solitons arise from the interplay of distinct phase transitions in the early universe. The breaking of the B−L symmetry generates magnetic flux tube strings—line-like defects threading through spacetime—while the spontaneously broken PQ symmetry produces flux-free superfluid vortices. Remarkably, the coupling between these two types of defects imparts a superconducting quality to the flux tubes and creates a metastable intertwined structure that resists conventional decay mechanisms. This topological locking lends the knots stability, allowing them to persist in a “knot-dominated era,” during which their energy density surpasses that of the surrounding radiation field.
Unlike radiation, whose energy density dilutes rapidly as the universe expands, the energy residing in these knot solitons diminishes more slowly, behaving like matter. Consequently, they folded into cosmic history a transient epoch wherein these intricate knots temporarily governed the energy budget of the universe. This era concluded when quantum tunneling—a counterintuitive quantum mechanical phenomenon permitting particles to surmount otherwise insurmountable energy barriers—enabled the knots to untangle and collapse. The decay process emitted copious heavy right-handed neutrinos, which then underwent asymmetric decays favoring matter over antimatter, injecting the cosmic inventory with a subtle imbalance that ultimately seeded all baryonic matter.
This cascade of events is deeply woven into the model’s mathematical architecture. Calculations account for the formation efficiency of knots, the mass scale of the heavy right-handed neutrinos (estimated around 10¹² GeV), and the resultant reheating temperature of approximately 100 GeV—a critical threshold corresponding to the final epoch when electroweak processes can transmute neutrino asymmetries into baryon asymmetries. This congruence with known physical scales boosts confidence in the model’s naturalness and explanatory power.
Moreover, the collapse of these cosmic knots leaves a distinct imprint on spacetime itself. The sudden disappearance of massive topological structures should have released gravitational waves with characteristic frequencies and intensities. The shape of the gravitational-wave spectrum would diverge significantly from standard cosmological backgrounds, potentially detectable by next-generation observatories such as the European Laser Interferometer Space Antenna (LISA), the U.S.-based Cosmic Explorer, and Japan’s Deci-hertz Interferometer Gravitational-wave Observatory (DECIGO). These facilities could, for the first time, listen in on echoes from a knot-dominated era, a rare empirical foothold into the enigmatic processes that set the matter-antimatter asymmetry.
Fundamentally, the concept of cosmic knots as topological solitons is profound. Solitons represent field configurations defined by invariants impervious to continuous deformation, ensuring stability despite the expanding and dynamic nature of the cosmos. This topology confers robustness to the proposed knot structures, insulating their theoretical existence from many variations in model parameters and making their predicted cosmological role compelling.
The researchers emphasize that while Kelvin’s original intuition—that atoms themselves might be knots—did not withstand the scrutiny of modern atomic physics, their work revitalizes knot theory in the context of cosmology and particle physics. Instead of knots constituting matter itself, the new model elevates cosmic knots as pivotal players in the genesis of matter. They are the primordial architects, the “grandparents” of matter, through their role in generating the heavy neutrinos whose decays sculpt the universe’s matter content.
Looking forward, the team acknowledges that much work remains. Refining theoretical frameworks and performing detailed numerical simulations will be essential to precisely forecast knot formation rates, decay dynamics, and the spectral features of the gravitational waves they emit. Establishing stronger connections between theoretical predictions and observational signatures will test the knot-dominated era hypothesis against empirical data. If forthcoming gravitational-wave experiments validate these predictions, it could signify a major paradigm shift in our understanding of cosmological evolution.
This union of topology, field theory, and cosmology not only unravels new paths to solving the baryon asymmetry problem but also opens innovative avenues for uncovering the nature of dark matter and the mass of neutrinos within a unified framework. The interdisciplinary reach of these discoveries stands to influence particle physics, astrophysics, and cosmology alike, propelling scientific inquiry toward a more complete narrative of the universe’s earliest moments and its progression to the complex cosmos we inhabit today.
The notion that knotted configurations of fields shaped our cosmic dawn eloquently intertwines mathematical elegance with physical reality, showcasing how revisiting historical ideas through the lens of modern science can reveal profound new insights. Its theoretical sophistication, potential observational signatures, and resolution of longstanding puzzles position this research as a milestone in the quest to decode the universe’s origins.
Subject of Research: Particle physics, cosmology, baryogenesis, and topological solitons
Article Title: Tying Knots in Particle Physics
News Publication Date: 29-Aug-2025
Web References: https://journals.aps.org/prl/abstract/10.1103/s3vd-brsn
References: Physical Review Letters, DOI: 10.1103/s3vd-brsn
Image Credits: Muneto Nitta/Hiroshima University
Keywords
Physics, Baryons, Leptons, Dark matter, Gravitational waves, Neutrinos, Solitons, Antimatter, Quantum tunneling
