### Speaker

Prof.
A.N. Ivanov
(TU Wien)

### Description

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 Poincar\'{e} gauge gravitational theory by Kibble
(T. W. B. Kibble, J. Math. Phys. {\bf 2}, 212 (1961)), where the
Einstein--Hilbert action can be represented in the same form ${\cal R}
= R + {\cal K}^2$.

### Primary author

Prof.
A.N. Ivanov
(TU Wien)

### Co-author

M. Wellenzohn
(TU Wien)