Isocurvature constraints on scalar dark matter production from the inflaton

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