Observational Properties of Feebly Coupled Dark Matter
  We show that decoupled hidden sectors can have observational consequences. As
a representative model example, we study dark matter production in the Higgs
portal model with one real singlet scalar $s$ coupled to the Standard Model
Higgs via $\lambda_{\rm hs}\Phi^\dagger\Phi s^2$ and demonstrate how the
combination of non-observation of cosmological isocurvature perturbations and
astrophysical limits on dark matter self-interactions imply stringent bounds on
the magnitude of the scalar self-coupling $\lambda_{\rm s}s^4$. For example,
for dark matter mass $m_{\rm s}=10$ MeV and Hubble scale during cosmic
inflation $H_*=10^{12}$ GeV, we find $10^{-4}\lesssim \lambda_{\rm s}\lesssim
0.2$.
