Axionic Landscape for Higgs Near-Criticality
  The measured value of the Higgs quartic coupling $\lambda$ is peculiarly
close to the critical value above which the Higgs potential becomes unstable,
when extrapolated to high scales by renormalization group running. It is
tempting to speculate that there is an anthropic reason behind this
near-criticality. We show how an axionic field can provide a landscape of
vacuum states in which $\lambda$ scans. These states are populated during
inflation to create a multiverse with different quartic couplings, with a
probability distribution $P$ that can be computed. If $P$ is peaked in the
anthropically forbidden region of Higgs instability, then the most probable
universe compatible with observers would be close to the boundary, as observed.
We discuss three scenarios depending on the Higgs vacuum selection mechanism:
decay by quantum tunneling; by thermal fluctuations or by inflationary
fluctuations.
