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 ${\mathrm{\Gamma }}_X$. We show that parametric resonance does not develop if ${\mathrm{\Gamma }}_X$ 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 ${\mathrm{\Gamma }}_X$ is smaller than about ${10}^{-3}{m}_X$.