Short description: Open problem concerning the imbalance of matter and antimatter in the universe

The quantum matter–antimatter asymmetry problem, also called the baryon asymmetry problem, is the open problem of explaining why the observable universe contains far more matter than antimatter. In the early universe, known physics suggests that matter and antimatter should have been produced in nearly equal amounts. If this had happened exactly, most particles and antiparticles would have annihilated into radiation, leaving little ordinary matter from which galaxies, stars, planets, and life could form.

The observed universe is instead dominated by matter. Antimatter exists in particle reactions and cosmic-ray processes, but there is no evidence for large antimatter galaxies or antimatter regions within the observable universe. Neither the Standard Model in its known form nor general relativity gives a complete explanation of this imbalance.^[1]^[2]

The problem is quantum-relevant because its proposed solutions involve particle interactions, quantum fields, CP violation, neutrinos, baryon-number violation, and early-universe nonequilibrium processes. The general class of mechanisms that could generate the excess of matter over antimatter is called baryogenesis.^[3]

The matter–antimatter asymmetry problem asks why a small early excess of matter survived annihilation and became the visible universe.

Basic idea

Matter and antimatter particles have the same mass but opposite charges and quantum numbers. When a particle meets its antiparticle, they can annihilate into radiation. In a perfectly symmetric early universe, equal amounts of matter and antimatter would have annihilated almost completely.

The existence of stars, galaxies, planets, and ordinary matter therefore implies that the early universe contained a tiny excess of matter over antimatter, or that some process generated such an excess before annihilation became complete.

The problem is to explain both the existence and the size of this excess. The imbalance is small compared with the number of photons in the cosmic microwave background, but it is large enough to account for all ordinary matter in the observable universe.

Sakharov conditions

In 1967, Andrei Sakharov identified three necessary conditions for producing a baryon asymmetry from an initially symmetric state.^[4] These are now called the Sakharov conditions:

baryon-number violation;
C-symmetry and CP-symmetry violation;
departure from thermal equilibrium.

Baryon-number violation is needed because the universe must produce more baryons than antibaryons. C and CP violation are needed because otherwise matter-producing and antimatter-producing reactions would balance each other. Departure from thermal equilibrium is needed because, in full thermal equilibrium, CPT symmetry would prevent a net baryon excess from developing.^[5]

Baryon-number violation

Baryon number is a quantum number that counts baryons minus antibaryons. Ordinary low-energy particle reactions appear to conserve baryon number. However, producing a cosmic matter excess requires some process that changes baryon number.

In the Standard Model, baryon number is conserved in ordinary perturbative processes, but it is not an exact symmetry nonperturbatively. Electroweak effects associated with anomalies can violate baryon plus lepton number. At high temperatures in the early universe, sphaleron processes may convert lepton asymmetry into baryon asymmetry.

Grand unified theories also allow baryon-number violation through very heavy hypothetical particles such as X and Y bosons. Such processes could generate a baryon asymmetry, but they are difficult to test directly because the relevant energy scales may be extremely high.

CP violation

CP violation means that the laws of physics do not treat matter and antimatter exactly as mirror-image opposites. It is essential for baryogenesis because, without CP violation, baryon-producing and antibaryon-producing processes would occur at equal rates.

CP violation was first observed in the neutral kaon system in 1964.^[6] In the Standard Model, CP violation appears in the quark mixing matrix, known as the CKM matrix. There may also be CP violation in the neutrino mixing matrix, known as the PMNS matrix, but this remains under experimental investigation.

The known CP violation in the Standard Model is not believed to be sufficient to explain the observed baryon asymmetry of the universe. This is one reason the matter–antimatter asymmetry problem points toward physics beyond the Standard Model.^[3]

Thermal nonequilibrium

The third Sakharov condition requires interactions to occur out of thermal equilibrium. In equilibrium, forward and reverse reactions balance each other, preventing a lasting matter excess from being generated.

The expansion of the early universe can provide nonequilibrium conditions. For example, if heavy particles decay more slowly than the universe expands, their decays can occur out of equilibrium and generate an asymmetry. Phase transitions in the early universe may also provide nonequilibrium conditions.^[7]

Baryogenesis

Baryogenesis is the name for mechanisms that generate the excess of matter over antimatter. Different baryogenesis models place the key physics at different energy scales.

In grand-unified baryogenesis, very heavy particles decay in a way that violates baryon number and CP symmetry. In electroweak baryogenesis, the asymmetry is generated near the electroweak phase transition. In leptogenesis, a lepton asymmetry is generated first and then partly converted into baryon asymmetry by electroweak sphaleron processes.

Leptogenesis is especially important because it connects the matter–antimatter asymmetry problem with neutrino physics. If heavy Majorana neutrinos existed in the early universe, their CP-violating decays could have produced a lepton asymmetry that later became a baryon asymmetry.

Baryon asymmetry parameter

The size of the asymmetry can be expressed using the baryon-to-photon ratio,

$η = \frac{n_{B} - n_{\bar{B}}}{n_{γ}},$

where $n_{B}$ is the baryon number density, $n_{\bar{B}}$ is the antibaryon number density, and $n_{γ}$ is the photon number density.

The photon number density for a thermal background at temperature $T$ is

$n_{γ} = \frac{1}{π^{2}} {(\frac{k_{B} T}{ℏ c})}^{3} 2 ζ (3) .$

At the present cosmic microwave background temperature, this corresponds to about 411 photons per cubic centimeter. A related and often useful quantity is the baryon asymmetry per entropy density,

$η_{s} = \frac{n_{B} - n_{\bar{B}}}{s} .$

The entropy density is

$s = \frac{2 π^{2}}{45} g_{*} (T) T^{3},$

where $g_{*} (T)$ counts the effective relativistic degrees of freedom at temperature $T$ . The observed asymmetry is very small, but it is not zero. Explaining this small nonzero value is the quantitative goal of baryogenesis models.

Antimatter regions

One possible idea is that the universe contains large matter-dominated and antimatter-dominated regions separated by vast distances. In such a scenario, the observable universe might appear matter-dominated only because nearby regions happen to contain matter.

This possibility is strongly constrained. At the boundaries between matter and antimatter regions, annihilation would produce gamma rays. No such boundary radiation has been observed. Current evidence therefore disfavors the existence of large antimatter domains within the observable universe.^[3]

Mirror anti-universe models

Another speculative possibility is that the Big Bang produced a universe–antiuniverse pair. In CPT-symmetric cosmological models, our universe could be paired with a mirror antiuniverse evolving in the opposite time direction.^[8]

Such models attempt to explain the matter dominance of our universe without requiring a conventional baryogenesis process inside a single universe. They remain speculative and must still reproduce the detailed observational successes of standard cosmology.

Cyclic and bounce models

In cyclic or bouncing cosmologies, the baryon asymmetry may be influenced by conditions before the hot expanding phase. Some models attempt to generate or amplify an asymmetry through asymmetric quantum bounces or earlier cosmological cycles.^[9]

These models are less established than standard baryogenesis scenarios, but they show how the matter–antimatter asymmetry problem connects with quantum cosmology.

Relation to neutrinos

Neutrinos may play an important role in the matter–antimatter asymmetry problem. If neutrinos are Majorana particles, then lepton number is not exactly conserved. Heavy Majorana neutrinos in the early universe could decay in CP-violating ways and produce a lepton asymmetry.

Electroweak sphaleron processes could then convert part of this lepton asymmetry into a baryon asymmetry. This mechanism is called leptogenesis. It links the matter–antimatter asymmetry problem to the neutrino mass problem, the origin of neutrino mass, and the search for neutrinoless double-beta decay.

Why it remains unsolved

The matter–antimatter asymmetry problem remains unsolved because the Standard Model contains some of the required ingredients but not enough to explain the observed asymmetry. It contains CP violation and nonperturbative baryon-number violation, but the amount of CP violation and the nature of the electroweak transition appear insufficient for the observed baryon asymmetry.

A successful explanation may require new particles, new CP-violating phases, lepton-number violation, high-scale baryon-number violation, a modified early-universe phase transition, or new cosmological structure.

Status

The matter–antimatter asymmetry problem remains one of the central open problems in particle physics and cosmology. The Sakharov conditions provide the general framework, but the actual mechanism that produced the observed imbalance is not known.

Leading possibilities include grand-unified baryogenesis, electroweak baryogenesis, leptogenesis, Affleck–Dine baryogenesis, and more speculative cosmological scenarios. Future progress may come from neutrino experiments, electric-dipole-moment searches, collider studies, gravitational-wave probes of early-universe phase transitions, and improved cosmological observations.