Gravitational production of scalar particles in inflationary-universe models

We study the production of massive scalar particles (with m$H_0$) in inflationary-universe models. A given mode of the scalar field is quantum mechanically excited when it is well within the Hubble radius (≡$H_0^{\mathrm{-}1}$) during the de Sitter phase of inflation. It then crosses outside the Hubble radius after which it is treated classically. Ultimately, long after reentering the Hubble radius, the fluctuations correspond to nonrelativistic scalar particles. The energy density in these particles depends on the Hubble parameter during inflation, the mass of the particle species, and the coupling of the scalar field to the curvature scalar. The energy density may contribute significantly to the total energy density in the Universe; in addition, new constraints to the value of the Hubble constant during inflation follow. As an example we apply our results to axions.