Stochastic Baryogenesis
  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 $H_\ast$ as
high as $10^{13}$ 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 $H_\ast$ is
favored by the isocurvature constraints.
