Classical inflaton field induced creation of superheavy dark matter

We calculate analytically and numerically the production of superheavy dark matter (X) when it is coupled to the inflaton field \phi within the context of a slow-roll m_\phi^2 \phi^2/2 inflationary model with coupling g^2 X^2 \phi^2/2. We find that X particles with a mass as large as 1000 H_i, where H_i is the value of the Hubble expansion rate at the end of inflation, can be produced in sufficient abundance to be cosmologically significant today. This means that superheavy dark matter may have a mass of up to 10^{-3} Planck mass. We also derive a simple formula that can be used to estimate particle production as a result of a quantum field's interaction with a general class of homogeneous classical fields. Finally, we note that the combined effect of the inflaton field and the gravitational field on the X field causes the production to be a nonmonotonic function of g^2.