Matter-Antimatter Asymmetry

• Matter-antimatter asymmetry is the imbalance between baryonic matter and antimatter, evidenced by a baryon-to-photon ratio of approximately 6×10⁻¹⁰.
• Dynamical mechanisms like GUT baryogenesis, electroweak baryogenesis, and leptogenesis rely on CP violation and non-equilibrium conditions to generate the excess of matter.
• Observational constraints from BBN, CMB anisotropies, and precision experiments underscore the need for physics beyond the Standard Model to explain this asymmetry.

The matter-antimatter asymmetry refers to the overwhelming dominance of baryonic matter over antimatter in the observed universe. Quantitatively, this is encoded in the baryon-to-photon ratio $$\eta_B = (n_B - n_{\bar{B}})/n_\gamma \approx 6 \times 10^{-10}$$ (BBN/CMB), indicating that, after accounting for all primordial annihilation and entropy generation, only one baryon per $10^{10}$ photons survives. The underlying mechanisms responsible for this excess have been studied within various frameworks, ranging from dynamical baryogenesis and leptogenesis models to novel topological, geometric, and kinematical scenarios. The Standard Model incorporates all ingredients of Sakharov's conditions but fails quantitatively; thus, most viable proposals invoke physics at high energy scales, cosmological phase transitions, or modifications of gravitational or field-theoretic structure.

1. Quantitative Observational Constraints

The empirical baryon-to-photon ratio $\eta_B$ is measured from Big Bang nucleosynthesis ($\eta_{\rm BBN} = (5.8 \pm 0.3) \times 10^{-10}$) and CMB anisotropies ($\eta_{\rm CMB} = (6.2 \pm 0.2) \times 10^{-10}$) (Canetti et al., 2012, Steigman et al., 2018). Absence of significant antihelium, antideuteron, or high-energy $\gamma$-ray annihilation signatures restricts the antimatter fraction in the galactic ISM to $f < 10^{-15}$ and in clusters to $f \lesssim 10^{-8}$ (Steigman et al., 2018). Lepton asymmetry in relic neutrino backgrounds is similarly constrained. The baryon asymmetry parameter, $\eta_B$, is not fine-tuned: successful structure, galaxy, and star formation is possible over many orders of magnitude variation, $10^{-22} \lesssim \eta_B \lesssim 10^{-3}$ (Steigman et al., 2018).

2. Sakharov Conditions and Dynamical Mechanisms

Any dynamical mechanism generating a net baryon number must satisfy three conditions (Canetti et al., 2012, Willmann et al., 2015, Garbrecht, 2018):

1. Baryon-number violation ($[B, H] \neq 0$): Processes such as sphaleron transitions, heavy particle decays, or instanton-induced transitions.
2. C and CP violation ($[CP, H] \neq 0$): Presence of complex phases in mixing matrices, trilinear couplings, loop-induced absorptive parts, or geometric background-induced asymmetries.
3. Departure from thermal equilibrium (or effective CPT violation): Achieved via phase transitions, cosmic expansion, or time-dependent backgrounds.

Standard baryogenesis scenarios include:

• GUT baryogenesis: Out-of-equilibrium decay of heavy bosons at $T \sim 10^{15}$ GeV.
• Electroweak baryogenesis: CP-violating reflection of quarks at a moving bubble wall during a strong first-order electroweak phase transition (Garbrecht, 2018).
• Leptogenesis: Decays of heavy Majorana neutrinos generate a lepton asymmetry, later converted by sphalerons (Garbrecht, 2018, Canetti et al., 2012).

The SM fails to produce sufficient $\eta_B$; e.g., CKM CP violation yields $\eta_B^{\rm SM} \lesssim 10^{-20}$ (Willmann et al., 2015).

3. Higgs Relaxation and Derivative Coupling Mechanisms

Recent measurement of $m_h$ implies a slow rise of the Higgs potential at large scales, possibly including a second minimum at $\phi \sim 10^{10}-10^{18}$ GeV (Kusenko et al., 2014, Kusenko, 2015).

• Postinflationary Higgs relaxation: The Higgs VEV relaxes after inflation, and its time-dependent condensate generates an effective chemical potential for lepton number via a dimension-six operator:

$$\mathcal{O}_6 = -\frac{1}{M_n^2}(\partial_\mu|\Phi|^2)j_{B+L}^\mu \implies \mu_{\rm eff}(t) = \frac{\partial_t | \phi(t)|^2}{M_n^2}$$

Lepton-number-violating processes via heavy Majorana neutrino exchange produce and wash out the asymmetry:

$$\frac{dn_L}{dt} + 3H n_L = -2 \frac{T^3}{\pi^2} \sigma_R \left( n_L - \frac{2}{\pi^2} \mu_{\rm eff} T^2 \right )$$

Electroweak sphalerons convert an established lepton asymmetry to baryons: $n_B = \frac{28}{79} n_L$ (Kusenko et al., 2014, Kusenko, 2015). Valid parameter ranges (e.g., $M_n \sim 10^{12}-10^{16}$ GeV, $T_R \sim 10^{13}$ GeV) yield $\eta_B \approx 10^{-10}$.

• Running Vacuum Coupling: A dimension-six derivative coupling to the running vacuum energy provides a CP-violating effective chemical potential (Lima et al., 2017):

$$\mathcal{L}_{\rm int} = \frac{1}{M_*^2} \partial_\mu \Lambda(H) J_B^\mu, \qquad \mu_B^{\rm eff} = -\frac{\dot{\Lambda}}{M_*^2}$$

The baryon-to-entropy ratio is analytically related to the time derivative of $\Lambda$ and the decoupling temperature $T_D$, matching observations for plausible $H_I / M_{\rm Pl}$ and $n$ parameters.

• Nonlinear Electrodynamics (NLED) models: Early universe dominated by non-linear electromagnetic fields, with baryogenesis sourced by a gravitational baryogenesis operator $\partial_\mu R J_B^\mu/M_*^2$, and the Ricci scalar $R$ evolving due to the NLED equation of state (Benaoum et al., 2021).

4. Geometric and Topological Scenarios

Several models generate $\eta_B \neq 0$ without explicit new fields, through geometric/topological effects:

• Rotating and Anisotropic Universes: In a rotating Bianchi IX background, global rotation and anisotropy induce a spectral splitting $\Delta E$ between particle and antiparticle modes of the Dirac field (Vardanyan, 16 Jul 2025). The difference acts as an effective chemical potential and is generically small but sufficient: $\Delta E / T \sim 10^{-10}$.
• de Sitter Kinematics: In global de Sitter spacetime, analytic continuation maps particle modes in one causal patch to antiparticle modes in the complementary wedge, yielding an observer-dependent matter-antimatter asymmetry even without dynamical generation (Gazeau et al., 22 Nov 2024).
• Brane/Domain-Wall Topology: Models with paired DW-aDW configurations in extra dimensions allow pair creation from gauge-field fluctuations with polarization along the extra dimension, depositing particle and antiparticle on separate branes and freezing in an asymmetry compatible with Planck $\eta_B$ values as the wall separation expands (Manousakis, 2022).

5. Quantum Statistical and Statistical Fluctuation Approaches

• Generation Model: Proposes that all leptons and quarks are composite, made from rishon–antirishon pairs, with exact conservation of a particle number $p$. The observed hydrogen-antihydrogen asymmetry arises as a Gaussian statistical fluctuation of order $\sigma \sim \sqrt{N}/2$ in many-body recombination processes, with no net matter excess over antimatter (Robson, 2016). Proton stability, absence of large-scale antimatter domains, and relic neutrino correlations are distinctive predictions.

6. Non-equilibrium Preheating, Solitons, and Multi-field Models

• Asymmetric Preheating: Explores resonant parametric amplification of modes during post-inflationary preheating, with CP-violating biases in the Floquet exponents or the kinetic/mass diagonalization matrix yielding exponential amplification of matter over antimatter (Enomoto et al., 2017). In multi-field setups, time-dependent unitary transformations mix CP phases so that the asymmetry is dynamically set and preserved through subsequent decay to baryons.
• Fragmentation into Oscillons: In models with complex inflaton and weakly broken global U(1) symmetry, the charge asymmetry generated during the end-of-inflation fragmentation is locked into non-topological solitons (oscillons) (Lozanov et al., 2014). Their subsequent decay sets $\eta_B$, and lattice simulations demonstrate the robustness of the lock-in mechanism.

7. Gravitational Mechanisms and Torsion Backgrounds

• Einstein–Cartan–Sciama–Kibble Theory: At ultrahigh densities, spacetime torsion induces a cubic Hehl–Datta term in the Dirac equation, flipping sign under charge conjugation and splitting energy levels between fermions and antifermions (Poplawski, 2011). The decay rates of heavy "archaeon" fermions and antiferimons are thereby biased, depositing baryons in the visible sector and antibaryons in a hidden (dark matter) sector, conserving total baryon number.
• Kalb–Ramond Torsion: In string-inspired cosmologies, a background axionic torsion $S_0$ shifts the dispersion relation for Majorana fermions in opposite directions for particles and antiparticles. The resulting equilibrium population difference is frozen in when lepton-number-violating processes decouple, and sphalerons transmute a fraction to baryons (Mavromatos et al., 2013). Axion mixing and two-loop effects can then generate suitable Majorana neutrino masses for leptogenesis.

8. Experimental and Low-energy Implications

Precision tests for new CP and CPT violation include (Willmann et al., 2015):

• Electric dipole moment searches (e.g., $d_e < 8.7 \times 10^{-29}$ e·cm for electron, $d_n < 3.0 \times 10^{-26}$ e·cm for neutron).
• Antiproton and antihydrogen spectroscopy (CPT invariance at $10^{-11}$-level).
• Muon $g-2$ anomaly ($\sim 0.5$ ppm discrepancy).
• Lepton-flavor-violating processes ($\mu^+ \rightarrow e^+ \gamma$ at $< 4 \times 10^{-13}$).
• Lorentz-invariance violation and gravity with antimatter.

Absence of significant signals at current sensitivities restricts many baryogenesis or CPT-violation extensions; future improvements in EDM, LFV, and antimatter gravity probe are essential for further discriminating mechanisms.

9. Impact, Synthesis, and Open Problems

Most successful baryogenesis and leptogenesis models can accommodate the observed $\eta_B$, but lack direct experimental verification due to the large mass scales (GUT or seesaw). Geometric, topological, and kinematic mechanisms offer alternative perspectives, where spacetime structure or statistical arguments seed asymmetry without explicit new particles. Some frameworks tie the origin of dark matter to hidden antimatter produced by the same process as visible baryogenesis (Poplawski, 2011, Dasgupta et al., 2019).

Open issues include:

• Pinning down the actual mechanism by connecting experiment (CP violation, neutrino properties, gravitational effects) to cosmological predictions.
• Distinguishing between dynamical baryogenesis and statistical/composite models.
• Quantifying non-equilibrium, soliton, or geometric effects in the context of inflation and preheating.

The matter-antimatter asymmetry remains a central target in cosmological theory and experiment, as its successful explanation interlocks baryon number violation, CP structure, cosmic dynamics, and possibly the dark sector.