Einstein-Cartan Gravity with Torsion Field Serving as Origin for
  Cosmological Constant or Dark Energy Density
  We analyse the Einstein-Cartan gravity in its standard form cal-R = R +
cal-K^2, where cal-R and R are the Ricci scalar curvatures in the
Einstein-Cartan and Einstein gravity, respectively, and cal-K^2 is the
quadratic contribution of torsion in terms of the contorsion tensor cal-K. We
treat torsion as an external (or a background) field and show that the
contribution of torsion to the Einstein equations can be interpreted in terms
of the torsion energy-momentum tensor, local conservation of which in a curved
spacetime with an arbitrary metric or an arbitrary gravitational field demands
a proportionality of the torsion energy--momentum tensor to a metric tensor, a
covariant derivative of which vanishes because of the metricity condition. This
allows to claim that torsion can serve as origin for vacuum energy density,
given by cosmological constant or dark energy density in the Universe. This is
a model-independent result may explain a small value of cosmological constant,
which is a long--standing problem of cosmology. We show that the obtained
result is valid also in the Poincare' gauge gravitational theory by Kibble (T.
W. B. Kibble, J. Math. Phys. 2, 212 (1961)), where the Einstein-Hilbert action
can be represented in the same form cal-R = R + cal-K^2.
