Scalar overproduction in standard cosmology and predictivity of non-thermal dark matter

Stable scalars can be copiously produced in the Early Universe even if they have no coupling to other fields. We study production of such scalars during and after (high scale) inflation, and obtain strong constraints on their mass scale. Quantum gravity-induced Planck-suppressed operators make an important impact on the abundance of dark relics. Unless the corresponding Wilson coefficients are very small, they normally lead to overproduction of dark states. In the absence of a quantum gravity theory, such effects are uncontrollable, bringing into question predictivity of many non-thermal dark matter models. These considerations may have non-trivial implications for string theory constructions, where scalar fields are abundant.