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It is shown that in most of the gauge theories with neutral currents an increase of fermion density leads to an increase of symmetry breaking. The symmetry behavior at a simultaneous increase of temperature and density is also investigated. It proves in particular that there was no symmetry restoration in the early universe if, at present, an excess of neutrinos over antineutrinos is sufficiently large.
Andrei Linde (Wed,) studied this question.