Higgs domain walls in the thermal background
  Most cosmological models predict that the universe was hot and dense at the
early stages of it's evolution. In this paper we analyse the influence of the
thermal bath of Standard Model particles on the dynamics of cosmological Higgs
domain walls. This manuscript poses an~extension of our earlier work in which
we investigated the evolution of networks of Higgs domain walls neglecting the
impact of temperature variation.
  Using the thermally corrected effective potential of Standard Model we have
found that both the position of the local maximum $h_{max}$ separating minima
and the width of domain walls strongly depend on temperature $T$. For
temperatures higher than $10^{10}\; \textrm{GeV}$ they respectively increase
proportionally and decrease inverse proportionally to the increasing
temperature. Thus, the energy scale of the problem follows the value of
temperature.
  Our numerical lattice simulations based on the PRS algorithm reveal that
Higgs domain walls in the presence of the background thermal bath are highly
unstable and decay shortly after formation. Moreover we have found that the
fraction of horizons produced by inflation in which Higgs field expectation
value is higher then $h_{max}$ needs to be very low in order for the evolution
of the~network of the domain walls to end in the electroweak vacuum. This means
that Higgs domain walls necessarily were very rare objects and their average
energy density was very small. As a result, the domain walls can not
significantly effect cosmological observables.
