  We study bulk viscosity arising from weak current Urca processes in dense
baryonic matter at and beyond nuclear saturation density. We consider the
temperature regime where neutrinos are trapped and therefore have nonzero
chemical potential. We model the nuclear matter in a relativistic density
functional approach, taking into account the trapped neutrino component. We
find that the resonant maximum of the bulk viscosity would occur at or below
the neutrino trapping temperature, so in the neutrino trapped regime the bulk
viscosity decreases with temperature as $T^{-2}$, this decrease being
interrupted by a drop to zero at a special temperature where the proton
fraction becomes density-independent and the material scale-invariant. The bulk
viscosity is larger for matter with lower lepton fraction, i.e., larger isospin
asymmetry. We find that bulk viscosity in the neutrino-trapped regime is
smaller by several orders of magnitude than in the neutrino-transparent regime,
which implies that bulk viscosity in neutrino-trapped matter is probably not
strong enough to affect significantly the evolution of neutron star mergers.
This also implies weak damping of gravitational waves emitted by the
oscillations of the postmerger remnant in the high-temperature,
neutrino-trapped phase of evolution.
