Graduate / Research-grade course

Baryogenesis: Why the Universe is Made of Matter

The profound asymmetry between matter and antimatter, the three Sakharov conditions, and the mechanisms that produced one baryon per ten billion photons in the primordial plasma.

9
Modules
15
Weeks
3
Sakharov
6e-10
Asymmetry Ξ·
GR
Level

Cosmic Timeline: Baryogenesis in the Early Universe

Matter-antimatter asymmetry emerges between inflation and BBN, at energies from 10^16 GeV down to ~100 GeV

Inflation10¹⁢ GeV10⁻³⁢ sReheating10¹⁡ GeV10⁻³² sGUT Baryo10ΒΉΒ² GeV10⁻²⁸ sLeptogenesis10⁹ GeV10⁻²⁴ sEW Phase Tr.100 GeV10⁻¹⁰ sQGP β†’ Hadrons150 MeV10⁻⁡ sBBN1 MeV1 sCMB/Today0.25 eV10ΒΉΒ³ sBARYOGENESIS ERAasymmetry \u03B7 = (n_B - n_Μ„B) / n_\u03B3 is set hereBefore: equal matter + antimattern_B = n_Μ„B\u2192After: tiny excess of matter (1 in 10^10)surviving baryon

Key Equations of Baryogenesis

Baryon Asymmetry

\(\displaystyle \eta \equiv \frac{n_B - n_{\bar B}}{n_\gamma} \approx 6 \times 10^{-10}\)

From Planck CMB and BBN constraints

Sakharov Conditions (1967)

1. Baryon number violation
2. C and CP violation
3. Departure from thermal equilibrium

Boltzmann Equation

\(\displaystyle \frac{dn_B}{dt} + 3H n_B = -\langle \sigma v \rangle (n_B^2 - n_{B,\mathrm{eq}}^2)\)

Jarlskog Invariant

\(\displaystyle J_{CP} = \mathrm{Im}\!\left[V_{us} V_{cb} V_{ub}^* V_{cs}^*\right] \approx 3\times10^{-5}\)

Sphaleron Rate (high T)

\(\displaystyle \Gamma_{\mathrm{sph}} \sim \alpha_W^5\, T^4\)

Davidson-Ibarra Bound

\(\displaystyle M_{N_1} \gtrsim 10^9~\mathrm{GeV}\)

For thermal leptogenesis

About This Course

One of the deepest questions in fundamental physics is why the observable universe contains matter at all. The laws of physics, as encoded in the Standard Model, are almost symmetric between particles and antiparticles β€” yet the observed universe consists almost entirely of matter, with an asymmetry of roughly one baryon per ten billion photons. This course examines the physics responsible for that tiny but consequential asymmetry.

We begin with the observational context (CMB, BBN), then derive Sakharov's three necessary conditions for baryogenesis. We cover the non-perturbative B+L violation via sphalerons, the CKM and PMNS matrices responsible for CP violation, the Boltzmann equations that describe departure from equilibrium, and four scenarios for generating the asymmetry: GUT baryogenesis, electroweak baryogenesis, leptogenesis, and Affleck-Dine.

Each module presents rigorous derivations (MathJax), schematic SVG diagrams of the underlying processes, and Python simulations of the key physics β€” from sphaleron rates to bubble-wall profiles to Boltzmann equation integrations for right-handed neutrino decay.

Module Outline

🌌
M0Cosmological ContextGraduate

The asymmetry problem, eta ~ 6e-10, thermal history, BBN + CMB constraints

Week 1
πŸ“
M1Sakharov's Three ConditionsGraduate

B violation, C and CP violation, out-of-equilibrium (1967)

Wk 2
βš›
M2Baryon Number ViolationGraduate

Instantons, sphalerons, anomaly, proton decay, B-L conservation

Wks 3–4
πŸͺž
M3CP ViolationGraduate

CKM matrix, Jarlskog invariant, neutral kaons, B-mesons, PMNS

Wks 5–6
🌑
M4Out-of-Equilibrium PhysicsGraduate

Boltzmann equation, decoupling, bubble nucleation, freeze-out

Wk 7
πŸš€
M5GUT BaryogenesisResearch

SU(5), SO(10), X-boson decays, inflationary dilution

Wks 8–9
⚑
M6Electroweak BaryogenesisResearch

First-order phase transition, bubble walls, BSM Higgs sector

Wks 10–11
🧫
M7LeptogenesisResearch

Right-handed neutrinos, seesaw, Davidson-Ibarra bound

Wks 12–13
πŸ”­
M8Observational ConstraintsGraduate

Planck, BBN, EDM experiments, proton decay, neutrinoless 2-beta

Wks 14–15

Related Courses

Quantum Field Theory

Anomalies, non-perturbative instantons, CP phases

Particle Physics

CKM matrix, neutrino masses, BSM extensions

Cosmology

Thermal history, BBN, inflation, reheating

Canonical Textbooks & References

β€’ Kolb, E. W. & Turner, M. S. β€” The Early Universe (Addison-Wesley, 1990). The foundational textbook for early-universe cosmology and baryogenesis.
β€’ Mukhanov, V. β€” Physical Foundations of Cosmology (Cambridge, 2005). Rigorous treatment of thermal history and Boltzmann equations.
β€’ Riotto, A. β€” "Theories of Baryogenesis", hep-ph/9807454 (1998). Classic review lectures covering GUT, EW, and leptogenesis scenarios.
β€’ Dine, M. & Kusenko, A. β€” "The Origin of the Matter-Antimatter Asymmetry", Rev. Mod. Phys. 76, 1 (2004).
β€’ Buchmuller, W., Di Bari, P. & Plumacher, M. β€” "Leptogenesis for Pedestrians", Annals Phys. 315, 305 (2005).
β€’ Cline, J. M. β€” "Baryogenesis", hep-ph/0609145 (2006). Les Houches lectures; modern and pedagogical.
β€’ Sakharov, A. D. β€” "Violation of CP-invariance, C asymmetry, and baryon asymmetry of the universe", JETP Lett. 5, 24 (1967). The original paper.
β€œAt present, the only explanation of the observed baryon asymmetry of the universe that does not invoke very special and finely tuned initial conditions rests on the three conditions formulated by Sakharov.”

β€” Kolb & Turner, The Early Universe

Begin Module 0: Cosmological Context β†’