Inflationary Imprints on Dark Matter

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.