Naturally Large Cosmological Neutrino Asymmetries in the MSSM

A large neutrino asymmetry is an interesting possibility for cosmology, which can have significant observable consequences for nucleosynthesis and the cosmic microwave background. However, although it is a possibility, there is no obvious reason to expect the neutrino asymmetry to be observably large. Here we note that if the baryon asymmetry originates via the Affleck-Dine mechanism along a d=4 flat direction of the MSSM scalar potential and if the lepton asymmetry originates via Affleck-Dine leptogenesis along a d=6 direction, corresponding to the lowest dimension directions conserving R-parity, then the ratio n_{L}/n_{B} is naturally in the range 10^{8}-10^{9}. As a result, a potentially observable neutrino asymmetry is correlated with a baryon asymmetry of the order of 10^{-10}.