Abstract
Using a multi-field stochastic approach, we investigate the vacuum expectation value (VEV) during inflation of a scalar field charged under a mildly broken global U(1) symmetry that can play the role of baryon or lepton number, or possibly a dark baryon number or a combination of the three. Even for a CP invariant Lagrangian, the stochastic distribution of inflationary VEVs in general breaks CP spontaneously, allowing for successful baryogenesis via the Affleck-Dine mechanism. For the Hubble scale during inflation H* as high as 1013 GeV, we show that the post-inflationary relaxation of the charged scalar with stochastic initial conditions can explain the observed baryon asymmetry, and that a charged scalar mass at the order of H* is favored by the isocurvature constraints.