  A striking feature of our universe is its near criticality. The cosmological
constant and weak hierarchy problems, as well as the metastability of the
electroweak vacuum, can all be understood as problems of criticality. This
suggests a statistical physics approach, based on the string landscape. We
present a dynamical selection mechanism for hospitable vacua based on search
optimization. Instead of focusing on stationary probability distributions, we
are interested in the approach to equilibrium. This is particularly relevant if
cosmological evolution has occurred for a time shorter than the
exponentially-long mixing time for the landscape. This imposes a strong
selection pressure among hospitable vacua, favoring those in regions where the
search algorithm is efficient. Specifically, the mean first passage time is
minimized for hospitable vacua lying at the bottom of funnel-like regions, akin
to the smooth folding funnels of proteins and the loss functions of
well-trained deep neural networks. The optimality criterion is
time-reparametrization invariant and defined by two competing requirements:
search efficiency, which requires minimizing the mean first passage time, and
sweeping exploration, which requires that random walks are recurrent. Optimal
landscape regions reach a compromise by lying at the critical boundary between
recurrence and transience, thereby achieving dynamical criticality. Remarkably,
this implies that the optimal lifetime of vacua coincides with the de Sitter
Page time. Our mechanism makes concrete phenomenological predictions: 1. The
expected lifetime of our universe is $10^{130}$ years, which is ~$2\sigma$ from
the Standard Model metastability estimate; 2. The SUSY breaking scale should be
high, $>10^{10}$ GeV. The present framework suggests a correspondence between
the near-criticality of our universe and non-equilibrium critical phenomena on
the landscape.
