  We introduce a new approach to the Higgs naturalness problem, where the value
of the Higgs mass is tied to cosmic stability and the possibility of a large
observable Universe. The Higgs mixes with the dilaton of a CFT sector whose
true ground state has a large negative vacuum energy. If the Higgs VEV is
non-zero and below $\mathcal{O}({\rm TeV})$, the CFT also admits a second
metastable vacuum, where the expansion history of the Universe is conventional.
As a result, only Hubble patches with unnaturally small values of the Higgs
mass support inflation and post-inflationary expansion, while all other patches
rapidly crunch. The elementary Higgs VEV driving the dilaton potential is the
essence of our new solution to the hierarchy problem. The main experimental
prediction is a light dilaton field in the 0.1-10 GeV range that mixes with the
Higgs. Part of the viable parameter space has already been probed by
measurements of rare B-meson decays, and the rest will be fully explored by
future colliders and experiments searching for light, weakly-coupled particles.
