  Through a mechanism similar to perturbative particle scattering, particles of
mass $m_\chi$ larger than the Hubble expansion rate $H_\mathrm{inf}$ during
inflation can be gravitationally produced at the end of inflation without the
exponential suppression powers of $\exp(-m_\chi/H_\mathrm{inf})$. Here we
develop an analytic formalism for computing particle production for such
massive particles. We apply our formalism to specific models that have been
previously been studied only numerically, and we find that our analytical
approximations reproduce those numerical estimates well.
