Baryon Asymmetry of the Universe (BAU)
The origin of the baryon asymmetry of the universe, namely the imbalance between matter and antimatter, is one of the central unsolved problems at the interface of particle physics and cosmology. In a perfectly symmetric universe, matter and antimatter would have been produced in equal amounts in the early hot plasma and would later have annihilated almost completely into radiation. The universe we observe is very different: galaxies, stars, planets, and ourselves are made of matter, while primordial antimatter is exceedingly rare. Observations of Big Bang Nucleosynthesis and the Cosmic Microwave Background indicate that the net number of baryons, normalized by the number of photons, is roughly six parts in ten billion [1]. This number is tiny, but it is cosmologically decisive. A small excess of matter over antimatter in the early universe is enough to account for essentially all ordinary matter that remains today. The broad theoretical framework that seeks to explain how such an excess was dynamically generated is called baryogenesis.
In 1967, Andrei Sakharov identified three necessary ingredients for producing a baryon asymmetry from an initially symmetric state [2]. These are now known as the Sakharov conditions. First, baryon number must be violated. If every microscopic reaction conserved baryon number exactly, the net baryon number of the universe could not change; any present asymmetry would have to be imposed as an initial condition. In an inflationary universe, however, any pre-existing baryon excess generated before or during inflation would be enormously diluted, so a successful scenario should generate the asymmetry after inflation, or at least after the relevant dilution has ended. Second, C and CP symmetries must be violated. C symmetry exchanges particles with antiparticles, while CP additionally includes spatial inversion. If these symmetries were exact, particle-producing and antiparticle-producing reactions would occur at equal rates, preventing a net excess from building up. Third, the relevant reactions must occur out of thermal equilibrium. In full equilibrium, forward and reverse reactions balance each other, and any newly produced asymmetry is erased as quickly as it appears. A departure from equilibrium is therefore needed to make the asymmetry irreversible on cosmological time scales.
The Standard Model of particle physics contains some of these ingredients, but not in a quantitatively sufficient form. Perturbative Standard Model interactions conserve baryon number, while nonperturbative electroweak processes associated with the chiral anomaly can violate baryon plus lepton number, B+L, while conserving baryon minus lepton number, B-L [3,4]. These processes, often described in terms of sphaleron transitions at high temperature, are extremely important in the early universe, but by themselves they do not provide a complete explanation of the observed baryon excess. The Standard Model also contains CP violation through the Kobayashi-Maskawa phase, but this effect is far too small to generate the observed asymmetry. Finally, for the measured Higgs boson mass, the electroweak transition in the Standard Model is not a strong first-order phase transition but a smooth crossover [5]. In such a crossover there are no expanding bubbles of a new phase, and hence no natural source of the strong out-of-equilibrium dynamics required for electroweak baryogenesis. For these reasons, explaining the baryon asymmetry strongly points to physics beyond the Standard Model. Below we describe three representative scenarios: GUT baryogenesis, leptogenesis, and electroweak baryogenesis. We then briefly discuss two additional scenarios that are especially relevant to recent developments.
GUT Baryogenesis
Baryogenesis based on Grand Unified Theories (GUTs) is one of the earliest and most elegant ideas for generating the matter-antimatter asymmetry [6]. GUTs attempt to unify the strong, weak, and electromagnetic interactions into a single force at extremely high energies, typically around 10^15-10^16 GeV. A characteristic feature of many such theories is that quarks and leptons are placed in common multiplets. As a result, interactions that transform quarks into leptons, or vice versa, can naturally violate baryon number. In the simplest SU(5) model, for example, extremely heavy gauge bosons conventionally called X and Y connect quarks and leptons [7]. Their decays can produce final states with different baryon and lepton numbers. If the decay rates into matter and antimatter channels differ because of CP-violating phases, the decays can leave behind a net baryon excess.
The three Sakharov conditions are realized in a very transparent way in this class of models. Baryon number violation is built into the GUT interactions themselves. New complex couplings beyond those of the Standard Model can provide CP violation. Departure from equilibrium can occur when the universe cools below the mass of the heavy GUT particles: their equilibrium abundance becomes exponentially suppressed, and once their interactions are slower than the cosmic expansion, they decay out of equilibrium. In this sense, GUT baryogenesis gives a simple physical picture: very massive particles, once common in the hot early universe, disappear through baryon-number-violating and CP-violating decays, leaving a small matter excess behind.
Despite its conceptual appeal, GUT baryogenesis faces serious challenges. The first is experimental testability. The GUT scale is far beyond the reach of any planned accelerator, so direct production of the relevant heavy particles is impossible. One indirect prediction of many GUTs is proton decay, because the same interactions that connect quarks and leptons can make the proton unstable. Minimal non-supersymmetric SU(5), for example, predicted proton decay at a rate that is already excluded. Super-Kamiokande and related searches have pushed the proton lifetime bounds above 10^34 years in important channels such as p -> e+ pi0 [8]. The non-observation of proton decay therefore strongly constrains the simplest GUT models and forces viable theories either to raise the relevant mass scale or to suppress the dangerous couplings.
A second challenge is the relation to inflation and reheating. If a baryon asymmetry is produced before inflation, it is diluted away. Thermal GUT baryogenesis therefore requires a reheating temperature high enough to produce the heavy GUT particles after inflation. If the reheating temperature is lower than the X and Y masses, the simplest thermal version of the mechanism cannot operate. A third issue is sphaleron washout. In minimal SU(5), the generated asymmetry conserves B-L. Since electroweak sphalerons later erase B+L while preserving B-L, an asymmetry with B-L = 0 would be washed out before the electroweak era ends. Successful high-scale baryogenesis therefore generally requires a mechanism that creates a nonzero B-L asymmetry, or a cosmological history in which the asymmetry is protected from sphaleron washout.
Thus, GUT baryogenesis remains a historically important and conceptually powerful idea, but it is constrained by proton decay searches, by the need for a sufficiently high reheating temperature, and by the requirement that the generated asymmetry survive electroweak sphaleron processes. A future observation of proton decay would be a profound indication of baryon-number violation and grand-unified physics, although identifying the precise baryogenesis mechanism would still require further theoretical and observational input.
Leptogenesis (LG)
Leptogenesis is a scenario in which the universe first generates an asymmetry in lepton number, rather than directly in baryon number, and then partially converts it into baryon number through electroweak sphaleron processes. The idea was proposed by Fukugita and Yanagida in the 1980s and has become one of the most compelling explanations of the baryon asymmetry because it links cosmology to the physics of neutrino masses [9]. In the Standard Model plasma above the electroweak scale, sphalerons are active and violate B+L while conserving B-L. Therefore, if some earlier process creates a nonzero B-L asymmetry, sphalerons redistribute it between baryons and leptons. In the Standard Model with three fermion generations and one Higgs doublet, roughly one third of an initial B-L asymmetry is converted into a baryon asymmetry [10].
The most familiar version is thermal leptogenesis with heavy right-handed Majorana neutrinos. These particles are natural ingredients of the seesaw mechanism, in which very heavy right-handed neutrinos make the observed left-handed neutrinos extremely light [11]. The heavy neutrinos can be produced in the hot early universe and later decay into leptons and Higgs bosons, or into the corresponding antiparticles. Because the neutrinos are Majorana particles, their decays violate lepton number. Because of CP-violating quantum effects, the decay rates into leptons and antileptons need not be equal. A small excess of leptons or antileptons is then produced, and sphaleron transitions convert part of that lepton asymmetry into the baryon asymmetry observed today.
In the simplest “vanilla” thermal leptogenesis picture, the lightest heavy neutrino is typically very massive, often above about 10^9 GeV [12]. This makes direct experimental detection unrealistic. Nevertheless, leptogenesis is attractive because it explains two mysteries at once: why neutrino masses are so small and why the universe contains more matter than antimatter. It also gives a clean role to B-L. Unlike many GUT baryogenesis models that generate only B+L, Majorana neutrino decays can generate B-L, which is precisely the combination preserved by sphalerons and therefore capable of surviving until late times.
The most important indirect test is the question of whether neutrinos are Majorana particles. If the light neutrinos are Majorana particles, lepton number is not an exact symmetry of nature, which is a key ingredient of the simplest leptogenesis models. Neutrinoless double beta decay would provide direct evidence for this property. Experiments such as KamLAND-Zen, LEGEND, and nEXO are therefore highly relevant to leptogenesis, even though they do not directly observe the heavy neutrinos responsible for the early-universe asymmetry. Recent KamLAND-Zen results have placed stringent limits on neutrinoless double beta decay in xenon [13]. A future discovery would strongly support the Majorana-neutrino framework, while continued non-observation would push the allowed parameter space to smaller effective masses or more model-dependent regions. It would not by itself exclude leptogenesis, since cancellations, normal ordering, flavor effects, or nonstandard realizations may still allow viable scenarios.
In summary, leptogenesis is a particularly appealing baryogenesis mechanism because it connects the matter-antimatter asymmetry to neutrino physics, a sector where the Standard Model is already known to be incomplete. Its main weakness is that the most economical versions operate at energy scales far beyond direct experimental reach. The scenario must therefore be tested indirectly through neutrino experiments, cosmological constraints, collider searches for low-scale variants, and possible gravitational-wave or topological-defect signatures in extended models.
Electroweak Baryogenesis (EWBG)
Electroweak baryogenesis is the idea that the baryon asymmetry was generated during the electroweak phase transition, when the Higgs field acquired its nonzero value and the weak interaction changed character [14]. This occurs at temperatures around 100 GeV, much lower than the GUT or standard leptogenesis scales. For this reason, electroweak baryogenesis is especially attractive experimentally: the new particles and interactions required by the mechanism may lie near the weak or TeV scale and can be tested by colliders, electric dipole moment experiments, Higgs precision measurements, and gravitational-wave searches.
The basic picture is as follows. If the electroweak phase transition is strongly first order, bubbles of the broken phase nucleate inside the surrounding symmetric phase. These bubbles expand and eventually fill the universe. The bubble walls provide an out-of-equilibrium environment, because particles in the plasma interact with a rapidly changing Higgs background. If new CP-violating interactions are present, particles and antiparticles can scatter differently from the bubble walls. This produces local chiral asymmetries in front of the wall. In the symmetric phase outside the bubbles, sphaleron transitions are still active and can convert these chiral asymmetries into baryon number. Inside the bubbles, where electroweak symmetry is broken, sphalerons must be sufficiently suppressed so that the newly created baryon asymmetry is not washed out.
The Standard Model itself cannot realize this scenario. With a 125 GeV Higgs boson, the electroweak transition is a crossover rather than a first-order transition. A successful model therefore needs additional ingredients that strengthen the transition. Many extensions do this by modifying the finite-temperature Higgs potential so that two phases can coexist and an energy barrier separates them. Adding a scalar singlet coupled to the Higgs is one of the simplest examples; two-Higgs-doublet models, supersymmetric models, and composite Higgs models can also provide the required structure. In effective descriptions, higher-dimensional Higgs interactions can similarly make the transition first order and can correlate baryogenesis with measurable deviations in the Higgs self-coupling [15].
The second required ingredient is new CP violation. The CP violation in the Standard Model is far too small, so electroweak baryogenesis requires additional CP-violating phases. In two-Higgs-doublet models, these phases can appear in the scalar potential or in Yukawa couplings. In supersymmetric models, phases in the chargino, neutralino, or scalar-quark sectors can become effective near the bubble wall. The microscopic computation is subtle: one must track how CP-violating interactions bias particle transport, how diffusion carries the asymmetry in front of the wall, and how sphalerons convert it into baryon number [16]. Conceptually, however, the mechanism is simple: the bubble wall acts as a moving filter that treats matter and antimatter slightly differently, and the electroweak plasma turns that local imbalance into a net baryon asymmetry.
Electroweak baryogenesis is constrained from several directions. New scalar particles that strengthen the phase transition can often be searched for directly at the LHC or indirectly through precision Higgs measurements. If the Higgs self-coupling deviates from the Standard Model prediction, it may indicate a modified Higgs potential of the kind needed for a first-order transition. Conversely, increasingly Standard-Model-like Higgs measurements restrict the available parameter space. New CP-violating phases are also strongly constrained by electric dipole moment experiments. Modern molecular EDM searches, including ACME and subsequent HfF+ measurements, have reached sensitivities that severely limit many simple electroweak baryogenesis models [17]. This has motivated ideas in which CP violation is time-dependent, hidden in a dark sector, active mainly during the phase transition, or otherwise arranged to avoid present-day EDM bounds.
At the same time, electroweak baryogenesis offers unusually rich observational possibilities. A strong first-order electroweak phase transition can generate a stochastic background of gravitational waves through bubble expansion, sound waves in the plasma, and turbulence. For an electroweak-scale transition, the peak frequency is typically in the range targeted by future space-based interferometers such as LISA and DECIGO [18]. A detection would provide a direct window into the thermal history of the universe near the weak scale and would strongly suggest new physics in the Higgs sector. A non-detection would also be valuable, because it would constrain the strength and duration of any first-order transition.
Thus, electroweak baryogenesis is highly predictive but highly constrained. It requires new physics both to strengthen the electroweak phase transition and to provide sufficient CP violation, yet these same ingredients are probed by colliders, EDM experiments, and future gravitational-wave detectors. This makes EWBG one of the most experimentally accessible baryogenesis scenarios, even though the allowed model space is becoming increasingly restricted.
Other Scenarios
Leptogenesis in the Presence of Density Perturbations
Standard leptogenesis calculations usually assume that the early universe is homogeneous on the scales relevant for the freeze-out of heavy particles. Recent work has pointed out that this assumption can miss an important effect when density or temperature perturbations are present [19]. The key observation is that the abundance of a heavy particle near freeze-out is extremely sensitive to the local temperature. Even modest perturbations can therefore have a nonlinear effect on the spatially averaged abundance. Hotter regions keep producing heavy particles slightly longer, while colder regions decouple earlier; because the dependence is exponential, the average is not the same as the result obtained from the average temperature alone.
This effect has been called acoustically driven freeze-out. Applied to leptogenesis, it can enhance the final spatially averaged lepton asymmetry. The mechanism does not replace the usual ingredients of leptogenesis, such as lepton-number violation and CP violation in heavy-neutrino dynamics. Rather, it modifies the cosmological environment in which freeze-out occurs. The result is that the baryon asymmetry can be larger than in the homogeneous calculation, and the lower bound on the heavy-neutrino mass can be relaxed in the presence of suitable perturbations [19]. This scenario is especially interesting because it connects particle-physics freeze-out to primordial inhomogeneities, opening a route by which early-universe structure could affect baryogenesis even before ordinary matter perturbations become visible.
Electromagnetic Leptogenesis (EMLG)
Electromagnetic leptogenesis is a variant of leptogenesis in which the relevant decays of heavy neutral leptons are mediated not primarily by the usual Yukawa interactions, but by electromagnetic dipole-type couplings [20]. In the original formulation, heavy electroweak-singlet neutrinos decay into light neutrinos and gauge bosons through effective dipole operators. CP violation arises from the interference between tree-level and loop-level decay amplitudes, and the resulting lepton asymmetry is then converted into baryon number by sphalerons, much as in standard leptogenesis.
A recent effective-field-theory treatment has sharpened this idea by enforcing full electroweak gauge invariance [21]. Before electroweak symmetry breaking, the relevant dipole operators must include the Higgs field. After symmetry breaking, they generate effective couplings of right-handed neutrinos to the photon, Z boson, and W boson. This makes electromagnetic leptogenesis naturally a low-scale, electroweak-window scenario, potentially operating around the TeV scale. The analysis also shows an important limitation: in a hierarchical, non-resonant regime, gauge invariance suppresses both the CP-odd source and the washout effects, making it difficult to reproduce the observed baryon asymmetry. The viable region therefore points toward quasi-degenerate right-handed neutrinos, where resonant enhancement and coherent flavor dynamics become essential.
The same recent work formulates the dynamics using Schwinger-Keldysh quantum kinetic equations, allowing decays, inverse decays, and scattering processes to be treated in a unified way without double counting [21]. Its broader importance, however, is that it embeds electromagnetic leptogenesis in a gauge-invariant EFT pipeline: the Wilson coefficients that control the early-universe dipole interactions can be matched and evolved down to the electroweak scale, and then connected to low-energy charged-lepton dipole observables such as μ -> eγ, the electron electric dipole moment, and the muon anomalous magnetic moment. This makes electromagnetic leptogenesis more than a mechanism for producing the baryon asymmetry; it provides a concrete bridge between the electroweak-era origin of matter and precision experiments that can constrain or test the same parameter space [21].
References
[1] N. Aghanim et al. (Planck Collaboration), Astron. Astrophys. 641, A6 (2020), arXiv:1807.06209.
[2] A. D. Sakharov, JETP Lett. 5, 24 (1967).
[3] G. 't Hooft, Phys. Rev. Lett. 37, 8 (1976); Phys. Rev. D 14, 3432 (1976).
[4] V. A. Kuzmin, V. A. Rubakov, and M. E. Shaposhnikov, Phys. Lett. B 155, 36 (1985).
[5] K. Kajantie, M. Laine, K. Rummukainen, and M. Shaposhnikov, Phys. Rev. Lett. 77, 2887 (1996), arXiv:hep-ph/9605288.
[6] M. Yoshimura, Phys. Rev. Lett. 41, 281 (1978); Erratum Phys. Rev. Lett. 42, 746 (1979).
[7] H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32, 438 (1974).
[8] A. Takenaka et al. (Super-Kamiokande Collaboration), Phys. Rev. D 102, 112011 (2020), arXiv:2010.16098.
[9] M. Fukugita and T. Yanagida, Phys. Lett. B 174, 45 (1986).
[10] J. A. Harvey and M. S. Turner, Phys. Rev. D 42, 3344 (1990).
[11] P. Minkowski, Phys. Lett. B 67, 421 (1977); T. Yanagida, Conf. Proc. C 7902131, 95 (1979); M. Gell-Mann, P. Ramond, and R. Slansky, Conf. Proc. C 790927, 315 (1979); R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. 44, 912 (1980).
[12] S. Davidson and A. Ibarra, Phys. Lett. B 535, 25 (2002), arXiv:hep-ph/0202239.
[13] S. Abe et al. (KamLAND-Zen Collaboration), Phys. Rev. Lett. 135, 262501 (2025), arXiv:2406.11438.
[14] A. G. Cohen, D. B. Kaplan, and A. E. Nelson, Ann. Rev. Nucl. Part. Sci. 43, 27 (1993), arXiv:hep-ph/9302210.
[15] C. Grojean, G. Servant, and J. D. Wells, Phys. Rev. D 71, 036001 (2005), arXiv:hep-ph/0407019.
[16] J. M. Cline, M. Joyce, and K. Kainulainen, JHEP 07, 018 (2000), arXiv:hep-ph/0006119.
[17] V. Andreev et al. (ACME Collaboration), Nature 562, 355 (2018); T. S. Roussy et al., Science 381, 46 (2023), arXiv:2212.11841.
[18] M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. Lett. 112, 041301 (2014), arXiv:1304.2433; C. Caprini et al., JCAP 04, 001 (2016), arXiv:1512.06239.
[19] K. Hotokezaka, R. Jinno, and R. Takada, Phys. Rev. D 111, 115029 (2025), arXiv:2501.10148.
[20] N. F. Bell, B. J. Kayser, and S. S. C. Law, Phys. Rev. D 78, 085024 (2008), arXiv:0806.3307.
[21] R. Takada, Phys. Rev. D, accepted (2026), arXiv:2603.01652, doi:10.1103/zq67-v2rj.