Positive Order $H^{2}$ Mass Corrections and Affleck-Dine Baryogenesis

It is usually assumed that the order H^2 corrections to the SUSY-breaking mass squared terms in the early Universe must be negative in order to allow the Affleck-Dine mechanism to work. We reconsider this assumption in the context of D-term inflation models for the case where the mass squared term has a correction cH^2 with c>0. We show that, in general, the baryon asymmetry is likely to be too small if c > 9/16. However, for c as large as 0.5 the observed baryon asymmetry can be readily generated; in particular, for d=6 directions the observed asymmetry can be produced for a wide range of reheating temperatures, in contrast with the case of negative H^2 corrections which require a reheating temperature around 1 GeV. Thus positive H^2 corrections do not rule out the Affleck-Dine mechanism and can even greatly broaden its applicability to inflation models