12.3 Matter-antimatter asymmetry

Matter-Antimatter Asymmetry in Cosmology

The universe is made almost entirely of matter, with virtually no antimatter. This is a deep puzzle: the standard model of particle physics predicts that the Big Bang should have produced equal amounts of both. If that had happened, matter and antimatter would have annihilated each other completely, leaving nothing but radiation. The fact that we exist at all means something tipped the balance. Understanding how that happened is one of the biggest open questions in cosmology.

Three conditions, proposed by physicist Andrei Sakharov in 1967, must all be met to generate this imbalance. Several competing mechanisms attempt to explain how those conditions were satisfied in the early universe, and none of them is fully confirmed yet.

The Observed Asymmetry

The universe around us is overwhelmingly matter. Antimatter shows up in cosmic rays and particle accelerators, but there are no large regions of antimatter anywhere we can detect. If whole antimatter galaxies existed, we'd see intense gamma-ray signatures at the boundaries where matter and antimatter meet. We don't.

Quantitatively, the asymmetry is tiny but decisive. For roughly every billion antimatter particles produced in the Big Bang, there were about a billion and one matter particles. After all the annihilation, that one-in-a-billion surplus is everything we see today: every star, planet, and atom. The standard model, as it stands, cannot account for even this small excess.

Sakharov Conditions for Asymmetry

In 1967, Andrei Sakharov identified three conditions that all must be satisfied for baryogenesis (the process that generates a net excess of matter over antimatter):

1. Baryon number violation — There must be physical processes that change the total baryon number. Baryon number is essentially a count of matter particles minus antimatter particles. If it were always conserved, you could never shift the balance from the equal starting point.

2. C and CP violation — Charge conjugation symmetry (C) and the combined charge-parity symmetry (CP) must be violated. C symmetry means swapping every particle for its antiparticle gives the same physics. CP symmetry means doing that swap and reflecting spatial coordinates gives the same physics. If both held perfectly, any process creating excess matter would be exactly mirrored by one creating excess antimatter, and no net asymmetry could develop.

3. Departure from thermal equilibrium — The universe must pass through a period out of thermal equilibrium. In perfect thermal equilibrium, every reaction runs equally fast in both directions, so any asymmetry that forms gets immediately washed out. A rapid phase transition or expansion can break equilibrium and "freeze in" the asymmetry.

All three conditions are necessary. Remove any one, and the asymmetry cannot be generated.

Mechanisms of Early Universe Baryogenesis

Several theoretical mechanisms have been proposed. Each satisfies the Sakharov conditions in a different way, and each has different experimental implications.

Electroweak baryogenesis occurs during the electroweak phase transition, when the unified electroweak force splits into the electromagnetic and weak forces (at temperatures around $10^{2}$ GeV). For this to work, the phase transition must be strongly first-order, meaning it happens abruptly through bubble nucleation rather than smoothly. CP-violating interactions at the bubble walls could then generate the asymmetry. The problem: in the standard model, the electroweak phase transition is not first-order, and the CP violation is far too small. New physics beyond the standard model would be required.

Leptogenesis takes an indirect route. Instead of generating a baryon asymmetry directly, it first creates an asymmetry in leptons (electrons, neutrinos, and their antiparticles). This lepton asymmetry is then partially converted into a baryon asymmetry through sphaleron processes, which are non-perturbative electroweak interactions that violate both baryon and lepton number while conserving their difference ($B - L$). The mechanism relies on the decay of very heavy Majorana neutrinos that violate both lepton number and CP symmetry. Leptogenesis is attractive because it connects naturally to the seesaw mechanism that explains why ordinary neutrinos have such tiny masses.

Affleck-Dine mechanism arises in supersymmetric theories. Scalar fields (the supersymmetric partners of quarks and leptons, called squarks and sleptons) can acquire large field values during inflation. As the universe cools and these fields decay, CP-violating interactions in the scalar potential generate a baryon asymmetry. This mechanism can produce a wide range of asymmetry values depending on the model parameters.

GUT baryogenesis operates at extremely high energies (around $10^{16}$ GeV), where grand unified theories predict that the strong, weak, and electromagnetic forces merge into a single force. At these energies, very heavy gauge bosons or Higgs bosons can decay in ways that violate baryon number and CP symmetry. This was historically the first baryogenesis mechanism proposed, but it faces challenges: the same GUT interactions that create the asymmetry can also cause proton decay, which has never been observed despite extensive searches.

CP Violation and the Matter-Antimatter Imbalance

CP violation is the linchpin of baryogenesis. Without it, matter and antimatter processes would proceed at identical rates, and no asymmetry could ever develop.

The standard model does contain CP violation, observed in the quark sector through a complex phase in the Cabibbo-Kobayashi-Maskawa (CKM) matrix, which describes how quarks mix between generations during weak interactions. This CP violation has been measured experimentally in decays of K mesons and B mesons. However, the amount is far too small to explain the observed matter-antimatter asymmetry, falling short by many orders of magnitude.

This gap is why physicists look to theories beyond the standard model:

• Supersymmetric models introduce many new CP-violating phases in the interactions of superpartner particles.
• Grand unified theories bring new heavy particles whose decays can violate CP in ways unavailable in the standard model.
• The neutrino sector may contain additional CP violation. If neutrinos are Majorana particles (their own antiparticles), CP-violating phases in the neutrino mixing matrix could drive leptogenesis.

Experimental efforts to pin down CP violation are active on multiple fronts. Studies of B meson decays at facilities like LHCb, searches for CP violation in neutrino oscillations at experiments like T2K and NOvA, and precision measurements of the electric dipole moments of particles (which would signal new CP-violating physics) all help constrain which baryogenesis mechanisms are viable. So far, no experiment has found enough CP violation to fully explain the asymmetry, keeping this one of cosmology's most pressing unsolved problems.