Einstein-Cartan Gravity with Torsion Field Serving as Origin for Cosmological Constant or Dark Energy Density

Understand

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.