Crunching Away the Cosmological Constant Problem: Dynamical Selection of
  a Small $\Lambda$
  We propose a novel explanation for the smallness of the observed cosmological
constant (CC). Regions of space with a large CC are short lived and are
dynamically driven to crunch soon after the end of inflation. Conversely,
regions with a small CC are metastable and long lived and are the only ones to
survive until late times. While the mechanism assumes many domains with
different CC values, it does not result in eternal inflation nor does it
require a long period of inflation to populate them. We present a concrete
dynamical model, based on a super-cooled first order phase transition in a
hidden conformal sector, that may successfully implement such a crunching
mechanism. We find that the mechanism can only solve the CC problem up to the
weak scale, above which new physics, such as supersymmetry, is needed to solve
the CC problem all the way to the UV cutoff scale. The absence of experimental
evidence for such new physics already implies a mild little hierarchy problem
for the CC. Curiously, in this approach the weak scale arises as the geometric
mean of the temperature in our universe today and the Planck scale, hinting on
a new "CC miracle", motivating new physics at the weak scale independent of
electroweak physics. We further predict the presence of new relativistic
degrees of freedom in the CFT that should be visible in the next round of CMB
experiments. Our mechanism is therefore experimentally falsifiable and
predictive.
