Baryogenesis conditions and model dependence

Let net baryon density mean baryon number carried by particles minus that carried by antiparticles, with a proton assigned unit baryon number. Divide by entropy density to define a yield that stays fixed during adiabatic expansion once baryon-changing reactions cease. The baryon-to-photon ratio is another useful normalization, but photon number can change during entropy transfer. Their familiar late-time conversion factor assumes the standard photon-neutrino entropy inventory and no additional late reheating.

Nucleosynthesis responds to nuclear reaction rates and the baryon density, while microwave anisotropies respond to baryon loading and the expansion model. Agreement between such inferences supports a consistent baryon abundance, conditional on the cosmological and microphysical model. Neither observable labels a particular heavy particle, CP phase, or phase transition as the cause. The nonzero abundance can be supplied as an initial condition for those later calculations even while its dynamical origin remains an open question.

Starting from a baryon-symmetric state, baryon-number-changing dynamics is required to create a total baryon excess. Charge conjugation and combined charge-conjugation-parity symmetries must be broken so opposite asymmetries are not produced with exactly compensating weights. Under the usual local, unitary, CPT-invariant framework with no imposed charge chemical potentials, complete thermal equilibrium cannot generate a baryon excess from the symmetric state. A departure from that equilibrium supplies the third standard Sakharov ingredient.

These conditions do not guarantee an adequate surviving abundance. A calculation must quantify the asymmetry source, inverse reactions, flavor redistribution, and washout. The existence of CP violation in laboratory particle physics alone does not demonstrate successful baryogenesis. Mechanisms that modify standard assumptions, such as an effective CPT-breaking background, require their own equilibrium argument instead of an unconditional appeal to the textbook list. A preexisting conserved charge also changes what an equilibrium ensemble is allowed to retain.

In the three-generation Standard Model, an electroweak transition between neighboring gauge vacua changes baryon and lepton number equally. Define the integer change of the usual unmultiplied Chern–Simons vacuum label as $\Delta N_{\rm CS}$. Then both charge changes equal three times that label change, while their difference is conserved. A thermal sphaleron rate is a transition rate per volume before conversion to charge relaxation; it must not be confused directly with the per-particle rates used earlier.

When electroweak sphalerons, the relevant Yukawa reactions, and gauge reactions equilibrate in the electroweak-symmetric plasma, chemical-potential constraints redistribute an initial baryon-minus-lepton yield. For three generations, one Higgs doublet, hypercharge neutrality, small chemical potentials, and no equilibrated additional charge-carrying species, the ideal result is a baryon fraction of twenty-eight seventy-ninths of that yield. Different equilibrium subsets, particle content, or passage through the electroweak crossover alter this conversion; it is not a universal leptogenesis efficiency.