Accessibility Measure for Eternal Inflation: Dynamical Criticality and
  Higgs Metastability
  We propose a new measure for eternal inflation, based on search optimization
and first-passage statistics. This work builds on the dynamical selection
mechanism for vacua based on search optimization proposed recently by the
author and Parrikar. The approach is motivated by the possibility that eternal
inflation has unfolded for a finite time much shorter than the exponentially
long mixing time for the landscape. The proposed accessibility measure assigns
greater weight to vacua that are accessed efficiently under time evolution. It
is the analogue of the closeness centrality index widely used in network
science. The proposed measure enjoys a number of desirable properties. It is
simultaneously time-reparametrization invariant, independent of initial
conditions, and oblivious to physical vs comoving weighing of pocket universes.
Importantly, the proposed measure makes concrete and testable predictions that
are largely independent of anthropic reasoning. Firstly, it favors vacua
residing in regions of the landscape with funnel-like topography, akin to the
energy landscape of naturally-occurring proteins. Secondly, it favors regions
of the landscape that are tuned at dynamical criticality, with vacua having an
average lifetime of order the de Sitter Page time. Thus the predicted lifetime
of our universe is of order its Page time, $\sim 10^{130}$ years, which is
compatible with Standard Model estimates for electroweak metastability.
Relatedly, the supersymmetry breaking scale should be high, at least $10^{10}$
GeV. The discovery of beyond-the-Standard Model particles at the Large Hadron
Collider or future accelerators, including low-scale supersymmetry, would rule
out the possibility that our vacuum lies in an optimal region of the landscape.
The present framework suggests a correspondence between the near-criticality of
our universe and dynamical critical phenomena on the string landscape.
