Stability of domain walls in models with asymmetric potentials
  We study the evolution of cosmological domain walls in models with asymmetric
potentials. Our research goes beyond the standard case of spontaneous breaking
of an approximate symmetry. When the symmetry is explicitly broken the
potential exhibits nearly degenerate minima which can lead to creation of a
metastable network of domain walls. The time after which the network will decay
depends on the difference of values of the potential in minima, its asymmetry
around the maximum separating minima and the bias of the initial distribution
of the field. Effect of asymmetry around the maximum separating minima is novel
one that we study with a new type of potential. Using numerical lattice
simulations we determine relative importance of these factors on decay time of
networks for generic potentials. We find that even very small departures from
the symmetric initial distribution case lead to rapid decay of the domain wall
network. As a result creation of a long lasting network capable of producing
observable gravitational wave signals is much more difficult than previously
thought. On the other hand details of the shape of the potential turn out to be
much less important than was expected and the evolution of network from
symmetric distribution is controlled by the difference of values of the
potential in the minima.
