Baryogenesis

The observable universe is overwhelmingly composed of matter, containing approximately baryons with virtually no anti-baryons. In the Standard Model, known sources of CP violation are insufficient to explain this asymmetry by about eight orders of magnitude. The CPT framework approaches this through topological dynamics during the universe's nucleation.

Chern-Simons Dynamics and Sakharov Conditions

During the nucleation of the S³ universe from a topological bubble, the Chern-Simons number undergoes rapid change. Since is not conserved during topology change, this naturally fulfills the first of Sakharov's conditions.

• Baryon number violation: Topological transitions on the S³ boundary violate baryon number.
• C and CP violation: While CPT is a discrete symmetry, C is broken by the Hopf orientation of the nucleating bubble.
• Out of equilibrium: The bubble nucleation event is rapid and far from thermal equilibrium.

The Rate Asymmetry

The CS term in the S³ action introduces a bias in the pair creation rate between matter and antimatter states during the rapid bubble growth phase. This leads to a rate asymmetry:

This leads to a numerical estimate for the baryon-to-photon ratio today:

The Asymmetry Carrier

While the rate asymmetry is established, the exact physical mechanism that converts this topological preference into a specific baryon orientation is the subject of the ongoing BN4 (Bubble Nucleation) programme.