  We investigate the gravitational production of a scalar field $\chi$ with a
mass exceeding the Hubble scale during inflation $m_\chi \gtrsim H_I$,
employing both analytical and numerical approaches. We demonstrate that the
steepest descent method effectively captures the epochs and yields of
gravitational production in a compact and simple analytical framework. These
analytical results align with the numerical solutions of the field equation.
Our study covers three spacetime backgrounds: de Sitter, power-law inflation,
and the Starobinsky inflation model. Within these models, we identify two
distinct phases of particle production: during and after inflation. During
inflation, we derive an accurate analytic expression for the particle
production rate, accounting for a varying Hubble rate. After inflation, the
additional burst of particle production depends on the inflaton mass around its
minimum. When this mass is smaller than the Hubble scale during inflation,
$H_I$, there is no significant extra production. However, if the inflaton mass
is larger, post-inflation production becomes the dominant contribution.
Furthermore, we explore the implications of gravitationally produced heavy
fields for dark matter abundance, assuming their cosmological stability.
