I will present a novel framework to solve simultaneously the electroweak hierarchy problem and the strong-CP problem. A small but finite Higgs vacuum expectation value and a small θ-angle are selected after the QCD phase transition, without relying on the Peccei-Quinn mechanism or other traditional solutions. This novel solution predicts a distinctive pattern of correlated signals at hadronic EDM, fuzzy dark matter and axion experiments. I will then discuss other incarnations of the mechanism in more generality, with different phenomenology, and attempt to draw a (relatively) unified picture of cosmological approaches to the Higgs hierarchy problem.

CERN and EPFL