Baryogenesis
Why Matter Survived
A Universe That Should Not Exist
Run the Big Bang forward using only what we know about particle physics, and you get nothing interesting. Hot, dense, full of energy – sure. But energy in the early universe materializes into matter and antimatter in exactly equal amounts. Every particle has a precise mirror twin. They should have annihilated each other completely as the universe cooled, leaving behind a thin haze of photons stretching forever into an empty void. No atoms, no stars, no planets, no rings to read this on. The default outcome of standard physics applied to the early universe is a universe nobody is around to notice.
Yet you exist. So does everything else made of matter, which is everything we can see. Something tipped the scales early on. For every billion matter-antimatter pairs, one extra matter particle was created without a partner. After the great annihilation, that lonely one-in-a-billion survivor was all that remained. Every star, every galaxy, every atom in your body is built from that residue. The number is precise. The cosmic microwave background and Big Bang nucleosynthesis both pin the baryon-to-photon ratio at roughly 6 in 1010, an asymmetry that cannot be a coincidence. Something dynamic happened. That something is called baryogenesis, and we still do not fully know what it was.
Three Conditions That Must Be Met
In 1967, Soviet physicist Andrei Sakharov, the same Sakharov who designed the Soviet hydrogen bomb and later became a dissident, asked a simple question. What conditions would a theory of physics need to satisfy in order to generate a matter-antimatter asymmetry from symmetric initial conditions? He found exactly three.
One: baryon number violation. Baryon number is the count of baryons (protons, neutrons, and their cousins) minus the count of antibaryons. If this number is rigorously conserved, the universe started with zero and must end with zero. Some physical process has to be able to change the count.
Two: C and CP violation. Charge conjugation (C) symmetry would swap particles for antiparticles. CP symmetry combines that with a mirror reflection of space. If physics obeys both C and CP perfectly, then for every process that produces extra matter, there is an exact mirror process that produces extra antimatter at the same rate. The two cancel. To produce a net imbalance, the laws of physics have to treat matter and antimatter slightly differently.
Three: departure from thermal equilibrium. In thermal equilibrium, every forward process runs at exactly the same rate as its reverse. Any asymmetry generated by a forward reaction would be erased by the reverse reaction running at the same rate. To freeze in an imbalance, the universe has to be evolving fast enough that some process gets out of equilibrium and leaves a permanent imprint.
All three conditions must be present simultaneously. Remove any one and the asymmetry vanishes. Sakharov's three-condition framework has dominated thinking about baryogenesis ever since.
The Standard Model Already Violates Baryon Number
Most people learn that the Standard Model conserves baryon number. In everyday processes it does – protons do not just turn into electrons, and neutrons inside stable nuclei do not vanish. But the Standard Model contains a subtle loophole, predicted theoretically in the 1970s and named sphalerons by Klinkhamer and Manton in 1984.
A sphaleron is a specific high-energy field configuration of the electroweak theory. Crossing through a sphaleron configuration changes baryon and lepton numbers by integer amounts simultaneously, while preserving their difference. In today's cold universe, the energy barrier to climb to a sphaleron is around 10 TeV. The probability of tunneling through it is astronomically suppressed. Sphalerons are, for all practical purposes, switched off today.
In the early universe, this was different. Before electroweak symmetry breaking, when temperatures exceeded roughly 100 GeV (about 1015 kelvin), sphalerons were not exotic exceptions but a routine background process. Baryon and lepton numbers were violated all the time, in every direction. The Standard Model, by itself, provides the first Sakharov condition for free at high temperature. The second condition is also partially satisfied: the CKM matrix, which describes how quarks mix during weak decays, has a measurable CP-violating phase. The third condition, departure from equilibrium, could in principle be provided by the electroweak phase transition as the universe cools through 100 GeV.
Why the Standard Model Alone Cannot Do It
The Standard Model has all three ingredients in principle, but the quantitative numbers fail by many orders of magnitude.
The CP violation in the CKM matrix is real but tiny. When you actually calculate how much baryon asymmetry it would generate during the electroweak phase transition, you get a number that is smaller than what we observe by at least ten orders of magnitude. Quark mixing simply does not violate CP enough to explain the universe.
The electroweak phase transition is worse. For a phase transition to drive the universe out of equilibrium strongly enough to lock in an asymmetry, it would need to be a first-order phase transition, like water freezing into ice with bubbles of the new phase nucleating violently inside the old phase. Lattice simulations done in the 1990s by Kajantie, Laine, Rummukainen, and Shaposhnikov showed that with the measured Higgs mass of 125 GeV, the Standard Model electroweak transition is not first-order at all. It is a smooth crossover, like fog gradually thickening. No bubble walls, no out-of-equilibrium chaos, no place to lock in an imbalance. Sphalerons keep running on both sides and erase whatever small asymmetry the CP violation manages to generate.
So the Standard Model fails on two counts: not enough CP violation, and the wrong kind of phase transition. The matter we are made of cannot have been produced by the physics in our current textbooks. Whatever generated the baryon asymmetry must lie outside the Standard Model. This is one of the cleanest, most quantitative pieces of evidence that new physics exists.
Leptogenesis – The Leading Candidate
The most popular proposal for baryogenesis works by going around the back. Instead of generating a baryon asymmetry directly, generate a lepton asymmetry first and let sphalerons convert part of it into a baryon asymmetry. This indirect route is called leptogenesis, proposed by Fukugita and Yanagida in 1986. It has gained enormous traction because it ties cleanly to a separate puzzle: why are neutrinos so absurdly light?
The leading explanation for neutrino mass is the seesaw mechanism, which postulates the existence of extremely heavy right-handed Majorana neutrinos – particles that are their own antiparticles, with masses possibly above 109 GeV. In the very early universe, these heavy neutrinos would have been produced abundantly. As the universe cooled, they would have decayed. Because Majorana neutrinos are their own antiparticles, their decays can in principle generate a net lepton asymmetry if CP is violated in the decay channels.
Then sphalerons take over. They are still active at the temperatures where heavy-neutrino decays would freeze in. They convert about a third of the lepton asymmetry into a baryon asymmetry. The remaining lepton asymmetry mostly escapes into the cosmic neutrino background, where it is too small to detect directly. The baryon asymmetry survives. As the universe cools further and electroweak symmetry breaks, the sphalerons switch off, and the baryon asymmetry is locked in permanently.
Leptogenesis is elegant. It uses one new ingredient – heavy Majorana neutrinos – to solve two problems at once: neutrino mass via the seesaw, and the baryon asymmetry via leptogenesis. It predicts that the heaviest of the three light neutrinos has a mass at most around 0.1 eV, comfortably consistent with the upper bound the cosmic microwave background sets on the sum of neutrino masses. The model requires that ordinary neutrinos be Majorana particles – the same as their antiparticles – which would show up experimentally as neutrinoless double beta decay. Experiments like KamLAND-Zen, GERDA, and the upcoming LEGEND-1000 are hunting for this signal. A confirmed detection would not prove leptogenesis directly but would strongly support its prerequisite. So far, nothing has been found.
Electroweak Baryogenesis – The Testable Alternative
A different family of models keeps baryogenesis at the electroweak scale, around 100 GeV, but adds new physics to fix the two Standard Model failures. The phase transition is upgraded from crossover to first-order by adding new scalar particles that modify the Higgs potential, often in supersymmetric or two-Higgs-doublet extensions. The CP violation is enlarged by introducing new phases beyond the CKM matrix – in supersymmetric chargino or neutralino sectors, or in extended Higgs sectors.
The appeal of electroweak baryogenesis is testability. The new physics has to live at energies the Large Hadron Collider can probe directly. If the model is right, the LHC or its successor should eventually find the new particles. So far, the LHC has not. As the experimental limits on supersymmetry, extra Higgs bosons, and exotic top-quark interactions have tightened through Run 2 and Run 3, the parameter space for electroweak baryogenesis has been steadily squeezed. The simplest minimal supersymmetric realizations are essentially ruled out. More elaborate two-Higgs-doublet versions remain viable but are increasingly constrained.
A first-order electroweak transition would also leave a gravitational wave signature, from bubble walls of the new phase colliding violently in the early universe. The frequency would land in the millihertz range, exactly where the LISA space-based gravitational wave detector is being built to look. LISA is scheduled to launch in the 2030s. If a stochastic gravitational wave background at the right frequency is detected with the right spectral shape, it would be powerful evidence that electroweak baryogenesis actually happened. Absence of such a signal would tighten the case against it.
Other Routes
Several less popular scenarios remain alive. GUT baryogenesis proposes that baryon number violation happened at much higher energies, around 1016 GeV, during the breaking of a grand unified theory that places quarks and leptons in the same multiplet. The scenario predicts proton decay at experimentally accessible rates, and decades of searching at Super-Kamiokande and other detectors have not found it. The simplest GUTs are ruled out; the more elaborate ones are pushed to lifetimes longer than current experiments can probe.
Affleck-Dine baryogenesis uses scalar fields carrying baryon number that develop large field values during inflation. As they decay after inflation ends, they produce baryon asymmetry directly. The scenario fits naturally into supersymmetric frameworks but requires specific scalar potentials that are not strongly motivated independently.
Asymmetric dark matter proposes that the dark matter sector also carries a conserved charge analogous to baryon number, generated together with the visible asymmetry by a shared mechanism. The model would explain the curious observational fact that the dark matter energy density is roughly five times the ordinary matter energy density – not vastly larger, not vastly smaller, but the same order. A shared origin would naturally produce ratios of order unity. Direct detection experiments and the lack of dark matter annihilation signals constrain the scenario but have not ruled it out.
Spontaneous CPT violation in the early universe would change the Sakharov framework entirely; it remains theoretical and speculative.
What Would Settle It
Three near-future experimental windows could decisively narrow the candidates.
Neutrinoless double beta decay. A confirmed detection by KamLAND-Zen, LEGEND-1000, nEXO, or another experiment would establish that neutrinos are Majorana particles – a prerequisite for leptogenesis. Combined with a measurement of the effective Majorana mass, it would feed directly into leptogenesis predictions.
LISA gravitational waves. A stochastic background at millihertz frequencies with the spectral shape of a first-order phase transition would point at electroweak baryogenesis. Silence would tighten the case against it.
Electric dipole moments. Many new-physics baryogenesis scenarios predict that the electron, neutron, or atomic nuclei should carry small but nonzero electric dipole moments – permanent separations of positive and negative charge along the spin axis. The ACME, JEDI, and nEDM experiments are pushing the limits down by orders of magnitude each decade. A detection would directly reveal new CP-violating physics; further null results would squeeze the surviving baryogenesis scenarios further.
None of these has produced a signal yet. The puzzle of why matter exists may take another generation of experiments to solve.
The Bigger Picture
The matter you are made of is the residue of an early universe accounting error. Some unknown process tipped a perfectly symmetric ledger by one part in a billion, and that surviving fraction built every structure we see. The accounting error itself is precisely measured. The accounting mechanism is not. Decades of theoretical work have given us a clean framework – the Sakharov conditions – and several detailed proposals for how to satisfy them, but no experiment has yet identified which one nature actually used.
Baryogenesis sits at the intersection of cosmology and particle physics, and any solution would link the early universe to physics beyond the Standard Model. It is one of the few experimentally clean indicators that the Standard Model is incomplete. The model fails not by giving wrong answers, but by giving an answer that flatly disagrees with the existence of a universe full of matter. Whatever extension nature has chosen, finding it would tell us what the laws of physics actually look like above the energies our colliders can reach. It would also answer one of the simplest possible questions about the universe: why is there anything here?
