  We study the effects on particle production of a Planck-suppressed coupling
between the inflaton and a scalar dark matter candidate, $\chi$. In the absence
of this coupling, the dominant source for the relic density of $\chi$ is the
long wavelength modes produced from the scalar field fluctuations during
inflation. In this case, there are strong constraints on the mass of the scalar
and the reheating temperature after inflation from the present-day relic
density of $\chi$ (assuming $\chi$ is stable). When a coupling $\sigma \phi^2
\chi^2$ is introduced, with $\sigma = {\tilde \sigma} m_\phi^2/ M_P^2 \sim
10^{-10} {\tilde \sigma}$, where $m_\phi$ is the inflaton mass, the allowed
parameter space begins to open up considerably even for ${\tilde \sigma}$ as
small as $\gtrsim 10^{-7}$. For ${\tilde \sigma} \gtrsim \frac{9}{16}$,
particle production is dominated by the scattering of the inflaton condensate,
either through single graviton exchange or the contact interaction between
$\phi$ and $\chi$. In this regime, the range of allowed masses and reheating
temperatures is maximal. For $0.004 < {\tilde \sigma} < 50$, constraints from
isocurvature fluctuations are satisfied, and the production from parametric
resonance can be neglected.
