Classical inflaton field induced creation of superheavy dark matter

We calculate analytically and numerically the production of superheavy dark matter (scalar field $X)$ when it is coupled to the inflaton field φ within the context of a slow-roll m_φ²φ²/2 inflationary model with coupling g²X²φ²/2. We find that X particles with a mass as large as 1000Hᵢ, where Hᵢ 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^-3MPl. 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 g².