  We show that dark matter abundance and the inflationary scale $H$ could be
intimately related. Standard Model extensions with Higgs mediated couplings to
new physics typically contain extra scalars displaced from vacuum during
inflation. If their coupling to Standard Model is weak, they will not
thermalize and may easily constitute too much dark matter reminiscent to the
moduli problem. As an example we consider Standard Model extended by a $Z_2$
symmetric singlet $s$ coupled to the Standard Model Higgs $\Phi$ via $\lambda
\Phi^{\dag}\Phi s^2$. Dark matter relic density is generated non-thermally for
$\lambda \lesssim 10^{-7}$. We show that the dark matter yield crucially
depends on the inflationary scale. For $H\sim 10^{10}$ GeV we find that the
singlet self-coupling and mass should lie in the regime $\lambda_{\rm s}\gtrsim
10^{-9}$ and $m_{\rm s}\lesssim 50$ GeV to avoid dark matter overproduction.
