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Baryogenesis
Baryogenesis
Baryogenesis
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In physical cosmology, baryogenesis (also known as baryosynthesis[1][2]) is the physical process that is hypothesized to have taken place during the early universe to produce baryonic asymmetry, the observation that only matter (baryons) and not antimatter (antibaryons) is detected in universe other than in cosmic ray collisions.[3][4]: 22.3.6  Since it is assumed in cosmology that the particles we see were created using the same physics we measure today, and in particle physics experiments today matter and antimatter are always symmetric, the dominance of matter over antimatter is unexplained.[5]

A number of theoretical mechanisms are proposed to account for this discrepancy, namely identifying conditions that favour symmetry breaking and the creation of normal matter (as opposed to antimatter). This imbalance has to be exceptionally small, on the order of 1 in every 1630000000 (≈2×109) particles a small fraction of a second after the Big Bang.[6] After most of the matter and antimatter was annihilated, what remained was all the baryonic matter in the current universe, along with a much greater number of bosons. Experiments reported in 2010 at Fermilab, however, seem to show that this imbalance is much greater than previously assumed.[7] These experiments involved a series of particle collisions and found that the amount of generated matter was approximately 1% larger than the amount of generated antimatter. The reason for this discrepancy is not yet known.

Most grand unified theories explicitly break the baryon number symmetry, which would account for this discrepancy, typically invoking reactions mediated by very massive X bosons (X) or massive Higgs bosons (H0
).[8] The rate at which these events occur is governed largely by the mass of the intermediate X or H0
 particles, so by assuming these reactions are responsible for the majority of the baryon number seen today, a maximum mass can be calculated above which the rate would be too slow to explain the presence of matter today.[9] These estimates predict that a large volume of material will occasionally exhibit a spontaneous proton decay, which has not been observed. Therefore, the imbalance between matter and antimatter remains a mystery.

Baryogenesis theories are based on different descriptions of the interaction between fundamental particles. Two main theories are electroweak baryogenesis,[10] which would occur during the electroweak phase transition, and the GUT baryogenesis, which would occur during or shortly after the grand unification epoch. Quantum field theory and statistical physics are used to describe such possible mechanisms.

Baryogenesis is followed by primordial nucleosynthesis, when atomic nuclei began to form.

Unsolved problem in physics
Why does the observable universe have more matter than antimatter?
More unsolved problems in physics

Background

[edit]

The majority of ordinary matter in the universe is found in atomic nuclei, which are made of neutrons and protons. There is no evidence of primordial antimatter. In the universe about 1 in 10,000 protons are antiprotons, consistent with ongoing production due to cosmic rays. Possible domains of antimatter in other parts of the universe is inconsistent with the lack of measurable of gamma radiation background.[5]: 36 

Furthermore, accurate predictions of Big Bang nucleosynthesis depend upon the value of the baryon asymmetry factor (see § Relation to Big Bang nucleosynthesis). The match between the predictions and observations of the nucleosynthesis model constrains the value of this baryon asymmetry factor. In particular, if the model is computed with equal amounts of baryons and antibaryons, they annihilate each other so completely that not enough baryons are left to create nucleons.[5]: 37 

There are two main interpretations for this disparity: either the universe began with a small preference for matter (total baryonic number of the universe different from zero), or the universe was originally perfectly symmetric, but somehow a set of particle physics phenomena contributed to a small imbalance in favour of matter over time. The goal of cosmological theories of baryogenesis is to explain the baryon asymmetry factor using quantum field theory of elementary particles.[5]: 37 

Sakharov conditions

[edit]

In 1967, Andrei Sakharov proposed[11] a set of three necessary conditions that a baryon-generating interaction must satisfy to produce matter and antimatter at different rates. These conditions were inspired by the recent discoveries of the cosmic microwave background[12] and CP-violation in the neutral kaon system.[13] The three necessary "Sakharov conditions" are:

Baryon number violation is a necessary condition to produce an excess of baryons over anti-baryons. But C-symmetry violation is also needed so that the interactions which produce more baryons than anti-baryons will not be counterbalanced by interactions which produce more anti-baryons than baryons. CP-symmetry violation is similarly required because otherwise equal numbers of left-handed baryons and right-handed anti-baryons would be produced, as well as equal numbers of left-handed anti-baryons and right-handed baryons.[5] Finally, the last condition, known as the out-of-equilibrium decay scenario, states that the rate of a reaction which generates baryon-asymmetry must be less than the rate of expansion of the universe. This ensures the particles and their corresponding antiparticles do not achieve thermal equilibrium due to rapid expansion decreasing the occurrence of pair-annihilation. The interactions must be out of thermal equilibrium at the time of the baryon-number and C/CP symmetry violating decay occurs to generate the asymmetry.[5]: 46 

In the Standard Model

[edit]

The Standard Model can incorporate baryogenesis, though the amount of net baryons (and leptons) thus created may not be sufficient to account for the present baryon asymmetry. There is a required one excess quark per billion quark-antiquark pairs in the early universe in order to provide all the observed matter in the universe.[3] This insufficiency has not yet been explained, theoretically or otherwise.

Baryogenesis within the Standard Model requires the electroweak symmetry breaking to be a first-order cosmological phase transition, since otherwise sphalerons wipe out any baryon asymmetry that happened up to the phase transition. Beyond this, the remaining amount of baryon non-conserving interactions is negligible.[14]

The phase transition domain wall breaks the P-symmetry spontaneously, allowing for CP-symmetry violating interactions to break C-symmetry on both its sides. Quarks tend to accumulate on the broken phase side of the domain wall, while anti-quarks tend to accumulate on its unbroken phase side.[15] Due to CP-symmetry violating electroweak interactions, some amplitudes involving quarks are not equal to the corresponding amplitudes involving anti-quarks, but rather have opposite phase (see CKM matrix and Kaon); since time reversal takes an amplitude to its complex conjugate, CPT-symmetry is conserved in this entire process.

Though some of their amplitudes have opposite phases, both quarks and anti-quarks have positive energy, and hence acquire the same phase as they move in space-time. This phase also depends on their mass, which is identical but depends both on flavor and on the Higgs VEV which changes along the domain wall.[16] Thus certain sums of amplitudes for quarks have different absolute values compared to those of anti-quarks. In all, quarks and anti-quarks may have different reflection and transmission probabilities through the domain wall, and it turns out that more quarks coming from the unbroken phase are transmitted compared to anti-quarks.

Thus there is a net baryonic flux through the domain wall. Due to sphaleron transitions, which are abundant in the unbroken phase, the net anti-baryonic content of the unbroken phase is wiped out as anti-baryons are transformed into leptons.[17] However, sphalerons are rare enough in the broken phase as not to wipe out the excess of baryons there. In total, there is net creation of baryons (as well as leptons).

In this scenario, non-perturbative electroweak interactions (i.e. the sphaleron) are responsible for the B-violation, the perturbative electroweak Lagrangian is responsible for the CP-violation, and the domain wall is responsible for the lack of thermal equilibrium and the P-violation; together with the CP-violation it also creates a C-violation in each of its sides.[18]

Relation to Big Bang nucleosynthesis

[edit]
See also: Baryon asymmetry

The central question to baryogenesis is what causes the preference for matter over antimatter in the universe, as well as the magnitude of this asymmetry. An important quantifier is the asymmetry parameter, given by

where nB and nB refer to the number density of baryons and antibaryons respectively and nγ is the number density of cosmic background radiation photons.[19]

According to the Big Bang model, matter decoupled from the cosmic background radiation (CBR) at a temperature of roughly 3000 kelvin, corresponding to an average kinetic energy of 3000 K / (10.08×103 K/eV) = 0.3 eV. After the decoupling, the total number of CBR photons remains constant. Therefore, due to space-time expansion, the photon density decreases. The photon density at equilibrium temperature T is given by with kB as the Boltzmann constant, ħ as the Planck constant divided by 2π and c as the speed of light in vacuum, and ζ(3) as Apéry's constant.[19] At the current CBR photon temperature of 2.725 K, this corresponds to a photon density nγ of around 411 CBR photons per cubic centimeter.

Therefore, the asymmetry parameter η, as defined above, is not the "best" parameter. Instead, the preferred asymmetry parameter uses the entropy density s, because the entropy density of the universe remained reasonably constant throughout most of its evolution. The entropy density is with p and ρ as the pressure and density from the energy density tensor Tμν, and g⁎ as the effective number of degrees of freedom for "massless" particles at temperature T (in so far as mc2 ≪ kBT holds), for bosons and fermions with gi and gj degrees of freedom at temperatures Ti and Tj respectively. At the present epoch, s = 7.04 nγ.[19]

Other models

[edit]

B-meson decay

[edit]

Another possible explanation for the cause of baryogenesis is the decay reaction of B-mesogenesis. This phenomenon suggests that in the early universe, particles such as the B-meson decay into a visible Standard Model baryon as well as a dark antibaryon that is invisible to current observation techniques.[20]

Asymmetric Dark Matter

[edit]

The asymmetric dark matter proposal investigates mechanisms that would explain the abundance of dark matter but lack of dark antimatter as the consequence of the same effect as would explain baryogenesis.[21]

See also

[edit]

References

[edit]
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Baryogenesis

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Baryogenesis refers to the physical processes in the early that generated the observed between and , resulting in a dominated by baryons (protons and neutrons) over antibaryons. This is quantified by the baryon-to-photon ratio, ηB≈6.1×10−10\eta_B \approx 6.1 \times 10^{-10}, as determined from measurements and constraints. Without such a process, the would have annihilated into shortly after the , leaving no ordinary to form , galaxies, or . The theoretical foundation for baryogenesis was established by in 1967, who outlined three necessary conditions for its occurrence: (1) processes that violate conservation, (2) charge conjugation (C) and charge-parity (CP) symmetry violation, and (3) interactions that depart from to prevent symmetric erasure of the asymmetry. These Sakharov conditions are satisfied in extensions of the of , where is not a fundamental symmetry but emerges from deeper unified theories. Baryogenesis must have occurred after cosmic inflation but before , typically at energy scales ranging from the electroweak scale (∼100\sim 100 GeV) to the grand unification scale (∼1016\sim 10^{16} GeV). Prominent mechanisms for baryogenesis include electroweak baryogenesis, which occurs during a strongly first-order electroweak . CP-violating interactions in the Higgs sector near advancing bubble walls generate a net or asymmetry out of equilibrium, which processes then partially convert into a by equilibrating and numbers while preserving B - L. Another key scenario is leptogenesis, where a asymmetry is first generated through the CP-violating out-of-equilibrium decays of heavy right-handed s at high temperatures, which is then partially converted into a by electroweak s. Grand unified theories (GUTs) also offer pathways, such as baryon-number-violating decays of superheavy gauge bosons or scalars during the GUT . These models connect baryogenesis to other unsolved puzzles, including masses, , and the . Experimental constraints on baryogenesis are indirect, arising from precision cosmology, collider searches for (e.g., at the LHC), and neutrino oscillation data that hint at leptogenesis viability. While the satisfies the Sakharov conditions in principle, its is insufficient by orders of magnitude to explain the observed ηB\eta_B, necessitating . Ongoing research explores testable predictions in supersymmetric extensions, , and flavored interactions.

Fundamentals

Definition and Motivation

Baryogenesis refers to the hypothetical physical processes in the early that produced a net , leading to the observed imbalance between s (such as protons and neutrons) and antibaryons. This asymmetry is characterized by the parameter η, defined as the ratio of the density n_B to the number density n_γ, with a present-day value of η ≈ 6.1 × 10^{-10}. This value, derived from measurements, indicates that for every billion s, there is roughly one excess over antibaryon. The parameter η was established during the epoch of baryogenesis, typically at high temperatures above the electroweak scale, and has remained nearly constant since the annihilation of electron-positron pairs around 10 seconds after the , as both s and s dilute similarly with cosmic expansion. The primary motivation for baryogenesis stems from the empirical fact that the is dominated by , with no evidence of large-scale domains. Astronomical observations, including searches for gamma-ray lines at 511 keV from positron-electron and analyses of fluxes, show no significant concentrations; antiprotons and other antiparticles in s are attributable to secondary production rather than primordial sources. Were the early perfectly symmetric in and , mutual would have converted nearly all baryonic into by the present era, leaving a featureless photon-dominated incompatible with the abundance of galaxies, stars, and ordinary . This asymmetry puzzle first gained prominence in the context of , as outlined in the 1948 paper by Alpher, Bethe, and Gamow, which predicted light element abundances assuming a hot, expanding early but implicitly required a net excess to match observations. The concept of baryogenesis as a dynamical process was formalized by in 1967, who introduced the term and argued that the imbalance could arise from fundamental interactions rather than ad hoc initial conditions. Probing baryogenesis thus bridges and cosmology, revealing connections to inflationary dynamics that homogenized the early , the composition of , and extensions beyond the needed to generate sufficient asymmetry.

Sakharov Conditions

In 1967, Andrei Sakharov proposed three essential conditions that must be satisfied for any physical process to generate a net baryon asymmetry in the universe, linking particle physics violations to cosmological evolution. These conditions—baryon number (B) violation, charge conjugation (C) and charge-parity (CP) symmetry violation, and departure from thermal equilibrium—provide the foundational criteria for viable baryogenesis mechanisms, ensuring that an initial symmetric state of matter and antimatter can evolve into the observed baryon excess, quantified by the baryon-to-photon ratio η≈6×10−10\eta \approx 6 \times 10^{-10}. The first condition requires processes that violate baryon number conservation, allowing transitions between states with different net baryon numbers (ΔB≠0\Delta B \neq 0). In the absence of such violations, the total baryon number would remain fixed, preventing the generation of a net asymmetry from an initially symmetric plasma; examples include non-perturbative effects in quantum field theories or high-energy interactions beyond the Standard Model. This violation enables the creation or annihilation of baryons and antibaryons in unequal numbers, setting the stage for asymmetry buildup. The second condition demands violations of C and CP symmetries, which ensure that the laws of physics distinguish between particles and their antiparticles in a way that favors one over the other. C violation alone would allow matter-antimatter transitions but symmetrically, while introduces differing interaction rates or decay probabilities for a particle and its CP-conjugate counterpart, such as Γ(X→f)≠Γ(Xˉ→fˉ)\Gamma(X \to f) \neq \Gamma(\bar{X} \to \bar{f}), where XX is a heavy particle and ff its decay products. Without CP violation, any B-violating process would produce equal numbers of baryons and antibaryons, maintaining overall symmetry. The third condition necessitates a departure from thermal equilibrium, where interactions occur out of balance, preventing the immediate erasure of any generated asymmetry. In full , the theorem dictates that forward and reverse reaction rates are equal, enforcing particle-antiparticle symmetry regardless of C or ; perturbations, such as the or phase transitions, drive the system away from equilibrium, allowing the asymmetry to persist and grow. For instance, if interaction rates Γ\Gamma are slower than the Hubble expansion rate HH, the system cannot equilibrate quickly enough to wash out imbalances. Mathematically, the net density evolution can be captured by ΔnB∝∫[Γ(B)−Γ(Bˉ)] dt\Delta n_B \propto \int [\Gamma(B) - \Gamma(\bar{B})] \, dt, where Γ(B)\Gamma(B) and Γ(Bˉ)\Gamma(\bar{B}) are the rates for baryon-producing and antibaryon-producing processes, respectively; the difference Γ(B)−Γ(Bˉ)\Gamma(B) - \Gamma(\bar{B}) arises from , and the integral over time requires non-equilibrium conditions to yield a non-zero result. Sakharov's framework, originally tied to weak interactions in the early , underscores how these conditions interplay in cosmological settings to explain the .

Standard Model Analysis

Baryon Asymmetry in the Standard Model

In the (SM) of , baryon number violation (B-violation) arises non-perturbatively through processes in the electroweak sector, mediated by instanton-like configurations in the SU(2)_L . These processes become active at high s, above the electroweak scale, and their rate is given by Γ/T4≈18αW5\Gamma / T^4 \approx 18 \alpha_W^5, where αW=g2/4π\alpha_W = g^2 / 4\pi is the weak and TT is the . This rate ensures rapid equilibration of during the early universe thermal bath, washing out any primordial asymmetry unless generated out-of-equilibrium. change by ΔB=nf\Delta B = n_f, where nf=3n_f = 3 is the number of families, linking B-violation to the . CP violation in the SM originates solely from the complex phase in the Cabibbo-Kobayashi-Maskawa (CKM) matrix, which parametrizes mixing. The magnitude of this CP violation is quantified by the Jarlskog invariant J≈3×10−5J \approx 3 \times 10^{-5}, a rephasing-invariant measure derived from the CKM elements that governs all quark-sector CP-violating amplitudes. This small value reflects the hierarchical structure of quark masses and mixings, limiting the strength of CP-violating effects at high energies. A potential mechanism for baryogenesis within the SM involves out-of-equilibrium conditions during the electroweak phase transition (EWPT), where the Higgs field acquires its , breaking SU(2)_L × U(1)Y to U(1){em}. However, lattice simulations confirm that the SM EWPT is a smooth crossover rather than a first-order transition, lacking the necessary bubble nucleation and to isolate regions from equilibration. Without a strong first-order transition, any CP-violating asymmetries generated via scatterings off the Higgs background cannot persist. Calculations of the generated in the SM, incorporating two-loop quantum corrections to quark-Higgs interactions and the CKM phase, yield a CP-violating ϵ≈10−6\epsilon \approx 10^{-6}, leading to a final asymmetry ηSM≈10−12\eta_{SM} \approx 10^{-12}, far below the observed value of η≈6×10−10\eta \approx 6 \times 10^{-10}. These estimates arise from the small Jarlskog invariant and damping effects from strong interactions, which suppress flavor-changing processes. The evolution of density nBn_B in the SM thermal bath is governed by Boltzmann equations of the form dnBdt+3HnB=∑i[Γi(ni−nieq)+ϵiΓinieq],\frac{dn_B}{dt} + 3 H n_B = \sum_i \left[ \Gamma_i (n_i - n_i^{eq}) + \epsilon_i \Gamma_i n_i^{eq} \right], where HH is the Hubble rate, Γi\Gamma_i are reaction rates (including and terms), nieqn_i^{eq} are equilibrium densities, and ϵi\epsilon_i encodes CP-violating contributions. This framework highlights how the interplay of B- and CP-violation with out-of-equilibrium dynamics fails quantitatively in the SM to produce the observed .

Limitations of Standard Model Mechanisms

The (SM) of particle physics fails to generate the observed primarily due to insufficient charge-parity ( in processes that could produce a net . In the context of electroweak baryogenesis, the CP-violating parameter ε, which measures the in particle production rates during the electroweak , is estimated as ε ≈ (g² / 16π²) sin δ_CKM (m_t² / M_W²), where g is the SU(2) coupling, δ_CKM is the CP-violating phase in the Cabibbo-Kobayashi-Maskawa matrix, m_t is the top quark mass, and M_W is the W boson mass. This yields ε ≈ 10^{-6} at best for realistic parameter values. However, subsequent entropy production from the expanding dilutes this , reducing the baryon-to-photon ratio η to ≈ 10^{-12}, far short of the observed value η ≈ 6 × 10^{-10} inferred from and data. A second critical limitation arises from the nature of the electroweak in the SM, which lattice simulations have established as a smooth crossover rather than a strong transition required for out-of-equilibrium conditions. The Higgs transition occurs at a critical T_c ≈ 100 GeV, but detailed calculations confirm it is second-order, with no or bubble nucleation. For successful baryogenesis, a transition demands v_c / T_c ≳ 1, where v_c is the Higgs at the transition; in the SM, however, v_c / T_c ≈ 0.3–0.6, insufficient to isolate regions of broken and prevent re-equilibration. This crossover behavior, verified through effective three-dimensional lattice formulations, precludes the necessary departure from . Sphaleron processes, which mediate violation via non-perturbative instanton-like configurations in the electroweak sector, further undermine SM baryogenesis by rapidly erasing any primordial . Above the electroweak scale, the transition rate Γ ≈ 18 α_W^5 T^4 (with α_W the weak and T the ) exceeds the Hubble expansion rate, ensuring efficient washout of with a relaxation time τ ≈ 1/Γ ≪ 1/H. These processes remain active until temperatures drop below ≈ 100 GeV, converting any pre-existing B + L (where B is and L is ) into zero net density unless suppressed by new physics. Collectively, these shortcomings yield an SM prediction for the of η_SM ≈ 10^{-12} or smaller, many orders of magnitude below observations and necessitating extensions beyond the SM for viable mechanisms. Recent lattice simulations, including those extending equation-of-state calculations up to electroweak scales by the HotQCD collaboration, reinforce the SM's inadequacy by confirming the absence of a strong and the persistence of rapid equilibration processes. As of 2025, these non-perturbative results underscore that no combination of SM parameters can amplify the sufficiently without additional dynamics.

Beyond-Standard-Model Theories

Grand Unified Theories

Grand Unified Theories (GUTs) propose a framework where the strong, weak, and electromagnetic forces unify into a single gauge interaction at an energy scale MGUT≈1016M_{\rm GUT} \approx 10^{16} GeV, extending the gauge group SU(3)C×_C \times SU(2)L×_L \times U(1)Y_Y. This unification introduces new heavy gauge bosons, such as the in SU(5) models, which mediate baryon-number-violating (ΔB=1\Delta B = 1) processes, enabling the generation of in the early universe. The primary mechanism for baryogenesis in GUTs involves the out-of-equilibrium decays of these superheavy particles at temperatures T≈MGUTT \approx M_{\rm GUT}, where the decay rate falls behind the Hubble expansion rate. For instance, an X can decay into a and a (X→q+lX \to q + l) or its charge conjugate, with the branching ratios differing due to arising from complex phases in the Yukawa couplings of the heavy fermions. These decays satisfy the Sakharov conditions through explicit ΔB≠0\Delta B \neq 0 interactions provided by the GUT gauge structure. The net baryon asymmetry is parameterized by the CP asymmetry in the decays, εX\varepsilon_X, which measures the difference in decay rates to baryon-producing versus antibaryon-producing channels. In minimal models, this is given by εX≈18πIm⁡[(YY†)ij2](YY†)ii,\varepsilon_X \approx \frac{1}{8\pi} \frac{ \operatorname{Im} [ (Y Y^\dagger)_{ij}^2 ] }{ (Y Y^\dagger)_{ii} }, where YY denotes the Yukawa coupling matrix involving the heavy fields. The observed baryon-to-entropy ratio η≈6×10−10\eta \approx 6 \times 10^{-10} can then be achieved as η≈(nX/s)εX\eta \approx (n_X / s) \varepsilon_X , with the initial number density of X bosons nXn_X tunable via their production during the GUT phase transition, allowing models to match cosmological observations. Specific implementations vary across GUT groups. In the minimal SU(5) model, facilitate ΔB=1\Delta B = 1 decays, but the theory conserves B−LB - L, making it vulnerable to washout by subsequent processes unless supplemented. SO(10) models extend this by incorporating right-handed neutrinos and a gauged U(1)B−LU(1)_{B-L} symmetry, providing a more robust framework where B−LB - L is initially conserved, protecting the until electroweak sphalerons partially convert it to net . In supersymmetric GUTs (SUSY-GUTs), the Affleck-Dine mechanism offers an alternative, where flat directions in the —corresponding to combinations of squark and slepton fields—develop large vacuum expectation values during , generating (or lepton) number through non-perturbative effects that break global symmetries. Challenges in GUT baryogenesis include constraints from proton decay searches. The Super-Kamiokande experiment imposes a lower bound on the proton lifetime of τp>2.4×1034\tau_p > 2.4 \times 10^{34} years (90% CL) for modes like p→e+π0p \to e^+ \pi^0, which directly limits the GUT scale via the exchange of bosons and requires MGUT≳1016M_{\rm GUT} \gtrsim 10^{16} GeV in viable models. Additionally, cosmic typically dilutes any primordial asymmetry generated at the GUT scale, necessitating post-inflationary mechanisms to regenerate it, such as reheating dynamics or late-decaying particles.

Electroweak Baryogenesis

Electroweak baryogenesis is a mechanism that generates the observed of the universe during the electroweak in the early universe, when the was around 100 GeV. This process relies on the 's transitions but requires extensions beyond the to produce a sufficiently strong and adequate . In the alone, the electroweak is a smooth crossover, which would allow sphalerons to erase any generated asymmetry, motivating the need for new physics to strengthen the transition. The core mechanism involves the and expansion of bubbles of the Higgs phase during a strong first-order electroweak . These bubbles form as the Higgs field tunnels from the symmetric phase to the broken phase, creating advancing walls that propagate through the plasma at velocities vwv_w typically supersonic, exceeding the cs=1/3c_s = 1/\sqrt{3}
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