Relaxing the Higgs mass and its vacuum energy by living at the top of
  the potential
  We consider an ultra-light scalar coupled to the Higgs in the presence of
heavier new physics. In the electroweak broken phase the Higgs gives a
tree-level contribution to the light-scalar potential, while new physics
contributes at loop level. Thereby, the theory has a cosmologically meta-stable
phase where the light scalar is around the top of its potential, and the Higgs
is a loop factor lighter than new physics. Such regions with precarious
naturalness are anthropically and environmentally selected, as regions with
heavier Higgs crunch quickly. We expect observable effects of rolling in the
dark-energy equation of state. Furthermore, vacuum energies up to the weak
scale can be canceled down to anthropically small values.
