Freezing-in the Hierarchy Problem

Models with a tiny coupling $\lambda$ between the dark matter and the Standard Model, $\lambda \sim v/M_\text{Pl}\sim 10^{-16}$, can yield the measured relic abundance through the thermal process known as freeze-in. We propose to interpret this small number in the context of perturbative large $N$ theories, where couplings are suppressed by inverse powers of $N$. Then $N \sim M_{\rm Pl}^2/v^2$ gives the observed relic density. Additionally, the ultimate cutoff of the Standard Model is reduced to $\sim 4\,\pi\, M_\text{Pl}/\sqrt{N} \sim 4\, \pi\, v$, thereby solving the electroweak hierarchy problem. These theories predict a direct relation between the Standard Model cutoff and the dark matter mass, linking the spectacular collider phenomenology associated with the low gravitational scale to the cosmological signatures of the dark sector. The dark matter mass can lie in the range from hundreds of keV to hundreds of GeV. Possible cosmological signals include washing out power for small scale structure, indirect detection signals from dark matter decays, and a continuous injection of electromagnetic and hadronic energy throughout the history of the Universe.