Isocurvature Constraints on Portal Couplings

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.