Baryon asymmetry

An important cosmological issue is the origin of the baryon asymmetry

$$\Delta B \sim \frac{n_B - n_{\bar{B}}}{n_\gamma} \sim 10^{-9}.$$ (15)

In the standard model sphaleron solutions describe tunneling between vacua with different $B$ at temperatures $T$ above the electroweak phase transition $T_{\rm EW} =$ O(100 GeV), which erase any preexisting baryon asymmetry with $B - L =0$. This includes asymmetries generated by the standard out-of-equilibrium decay scenario for heavy colored scalars in grand unified theories. It is possible that an asymmetry is regenerated by the standard model sphaleron effects at the time of the electroweak transition (e.g., in processes involving expanding bubble walls), but the necessary CP violation and out of equilibrium constraints are not satisfied in the standard model or the MSSM.

One attractive scenario involves the initial generation of a nonzero lepton asymmetry (or an assymetry in $B-L$) in the early universe, which is then converted into comparable baryon and lepton asymmetries by sphalerons during the electroweak transition. For example, the heavy Majorana neutrino $N$ expected in seesaw models may have asymmetric decays into a Higgs scalar $h$ and neutrino [48]

$$\Gamma (N \mbox{$\rightarrow$}h \nu) \ne \Gamma(N \mbox{$\rightarrow$}h \bar{\nu})$$ (16)

if there is sufficient leptonic CP violation, leading to a nonzero $\Delta L$, which is later converted to $\Delta B \ne 0$ and $\Delta L \ne 0$. Such scenarios place constraints which are in principle stringent on the ($L$-violating) neutrino masses, to avoid wiping out both $\Delta B$ and $\Delta L$ [48], typically $m_\nu < {\rm O}(1-10)$ eV, but with large theoretical uncertainties. This applies to $\nu_\tau$ and $\nu_\mu$ as well as $\nu_e$.