  In this paper, we studied the full Einstein-Hilbert actions with respect to
non-symmetric metrics and the corresponding torsion.
  The first concrete result in this paper are the general formulae for pressure
and density with respect to the Madsen's article (the equation (3.1), in [10]).
Based on these results, we obtained the expression of energy-momentum tensor
with respect to non-symmetric metrics.
  We started the generalization of the Bianchi type-I model of cosmology with
respect to the corresponding non-symmetric metrics.
