EINSTEIN–CARTAN GRAVITY WITH TORSION FIELD SERVING AS AN ORIGIN FOR THE COSMOLOGICAL CONSTANT OR DARK ENERGY DENSITY

Abstract

We analyse the Einstein–Cartan gravity in its standard form  = R +  2 , where  and R are the Ricci scalar curvatures in the Einstein–Cartan and Einstein gravity, respectively, and  2 is the quadratic contribution of torsion in terms of the contorsion tensor  . We treat torsion as an external (or background) field and show that its contribution 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 owing to the metricity condition. This allows us to claim that torsion can serve as an origin for the vacuum energy density, given by the cosmological constant or dark energy density in the universe. This is a model-independent result that may explain the small value of the cosmological constant, which is a long-standing problem in cosmology. We show that the obtained result is valid also in the Poincaré gauge gravitational theory of Kibble, where the Einstein–Hilbert action can be represented in the same form:  = R +  2 .