  We study sterile neutrinos in an extension of the standard model, based on
the gauge group $SU(3)_C\otimes SU(3)_L\otimes SU(3)_R\otimes U(1)_N$, and use
this model to illustrate how to apply cosmological limits to thermalized
particles that decouple while relativistic. These neutrinos, $N_{aL}$, can be
dark matter candidates, with a keV mass range arising rather naturally in this
model. We analyse the cosmological limits imposed by $N_{eff}$ and dark matter
abundance on these neutrinos. Assuming that these neutrinos have roughly equal
masses and are not CDM, we conclude that the $N_{eff}$ experimental value can
be satisfied in some cases and the abundance constraint implies that these
neutrinos are hot dark matter. With this information, we give upper bounds on
the Yukawa coupling between the sterile neutrinos and a scalar field, the
possible values of the VEV of this scalar field and lower bounds to the mass of
one gauge boson of the model.
