  We consider the linearized nonsymmetric theory of gravitation (NGT) within
the background of an expanding universe and near a Schwarzschild mass. We show
that the theory always develops instabilities unless the linearized
nonsymmetric lagrangian reduces to a particular simple form. This form contains
a gauge invariant kinetic term, a mass term for the antisymmetric metric-field
and a coupling with the Ricci curvature scalar. This form cannot be obtained
within NGT. Based on the linearized lagrangian we know to be stable, we
consider the generation and evolution of quantum fluctuations of the
antisymmetric gravitational field (B-field) from inflation up to the present
day. We find that a B-field with a mass m ~ 0.03(H_I/10^(13)GeV)^4 eV is an
excellent dark matter candidate.
