  We consider portal models which are ultraweakly coupled with the Standard
Model, and confront them with observational constraints on dark matter
abundance and isocurvature perturbations. We assume the hidden sector to
contain a real singlet scalar $s$ and a sterile neutrino $\psi$ coupled to $s$
via a pseudoscalar Yukawa term. During inflation, a primordial condensate
consisting of the singlet scalar $s$ is generated, and its contribution to the
isocurvature perturbations is imprinted onto the dark matter abundance. We
compute the total dark matter abundance including the contributions from
condensate decay and nonthermal production from the Standard Model sector. We
then use the Planck limit on isocurvature perturbations to derive a novel
constraint connecting dark matter mass and the singlet self coupling with the
scale of inflation: $m_{\rm DM}/{\rm GeV}\lesssim 0.2\lambda_{\rm
s}^{\scriptscriptstyle 3/8} \left(H_*/10^{\scriptscriptstyle 11}{\rm
GeV}\right)^{\scriptscriptstyle -3/2}$. This constraint is relevant in most
portal models ultraweakly coupled with the Standard Model and containing light
singlet scalar fields.
