  The helicity evolution of a neutrino interacting with randomly moving and
polarized matter is studied. We derive the equation for the averaged neutrino
helicity. The type of the neutrino interaction with background fermions is not
fixed. In the particular case of a tau-neutrino interacting with
ultrarelativistic electron-positron plasma we obtain the expression for the
neutrino helicity relaxation rate in the explicit form. We study the neutrino
spin relaxation in the relativistic primordial plasma. Supposing that the
conversion of left-handed neutrinos into right-handed ones is suppressed at the
early stages of the Universe evolution we get the upper limit on the
tau-neutrino mass.
