  We investigate the production of a spectator scalar dark matter field that is
directly coupled to the inflaton during inflation and reheating. We consider
two specific inflationary potentials, namely the Starobinsky and T-model of
inflation, which satisfy the constraints on the scalar tilt, $n_s$, and
tensor-to-scalar ratio, $r$, measured by the Planck satellite. Excitation of
light scalar dark matter during inflation may result in large isocurvature
perturbations, which can be avoided by inducing a sizable effective dark matter
mass during the inflationary phase. For purely gravitational production, the
Planck isocurvature constraints require the dark matter mass to be larger than
the Hubble scale at horizon exit, with $m_{\chi} \gtrsim 0.5H_*$. For small
bare dark matter masses $m_{\chi} \ll H_*$, these constraints translate into a
lower bound on the dark matter coupling to the inflaton. We argue that these
constraints can be applied to a wide class of single-field slow-roll inflation
models. We also derive isocurvature, dark matter abundance, and Lyman-$\alpha$
constraints on the direct coupling and bare dark matter mass.
