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

TL;DR

This paper proposes that torsion in Einstein-Cartan gravity can serve as the origin of the cosmological constant or dark energy, offering a model-independent explanation for the small observed value of vacuum energy.

Contribution

It demonstrates that torsion acts as a source of vacuum energy density, linking it to the cosmological constant or dark energy in a way that is independent of specific models.

Findings

Torsion energy-momentum tensor is proportional to the metric tensor.

Torsion can serve as the origin of vacuum energy density.

Result applies to Einstein-Cartan and Poincaré gauge gravity theories.

Abstract

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.