The fine tuning of the cosmological constant in a conformal model
  We consider a conformal model involving two real scalar fields in which the
conformal symmetry is broken by a soft mechanism and is not anomalous. One of
these scalar fields is representative of the standard model Higgs. The model
predicts exactly zero cosmological constant. In the simplest version of the
model, some of the couplings need to be fine tuned to very small values. We
formulate the problem of fine tuning of these couplings. We argue that the
problem arises since we require a soft mechanism to break conformal symmetry.
The symmetry breaking is possible only if the scalar fields do not evolve
significantly over the time scale of the Universe. We present two solutions to
this fine tuning problem. We argue that the problem is solved if the classical
value of one of the scalar fields is super-Planckian, i.e. takes a value much
larger than the Planck mass. The second solution involves introduction of a
strongly coupled hidden sector that we call hypercolor. In this case the
conformal invariance is broken dynamically and triggers the breakdown of the
electroweak symmetry. We argue that our analysis applies also to the case of
the standard model Higgs multiplet.
