GUT baryogenesis after preheating: numerical study of the production and   decay of X-bosons
  We perform a fully non-linear calculation of the production of supermassive Grand Unified Theory (GUT) $X$ bosons during preheating, taking into account the fact that they are unstable with a decay width $\Gamma_X$. We show that parametric resonance does not develop if $\Gamma_X$ is larger than about $10^{-2} m_X$. We compute the nonthermal number density of superheavy bosons produced in the preheating phase and demonstrate that the observed baryon asymmetry may be explained by GUT baryogenesis after preheating if $\Gamma_X$ is smaller than about $10^{-3} m_X$. 
E.W. Kolb, A. Riotto and I.I. Tkachev