Weyl-Cartan-Weitzenb\"{o}ck gravity as a generalization of teleparallel
  gravity
  We consider a gravitational model in a Weyl-Cartan space-time, in which the
Weitzenb\"{o}ck condition of the vanishing of the sum of the curvature and
torsion scalar is also imposed. Moreover, a kinetic term for the torsion is
also included in the gravitational action. The field equations of the model are
obtained from a Hilbert-Einstein type variational principle, and they lead to a
complete description of the gravitational field in terms of two fields, the
Weyl vector and the torsion, respectively, defined in a curved background. The
cosmological applications of the model are investigated for a particular choice
of the free parameters in which the torsion vector is proportional to the Weyl
vector. Depending on the numerical values of the parameters of the cosmological
model, a large variety of dynamic evolutions can be obtained, ranging from
inflationary/accelerated expansions to non-inflationary behaviors. In
particular we show that a de Sitter type late time evolution can be naturally
obtained from the field equations of the model. Therefore the present model
leads to the possibility of a purely geometrical description of the dark
energy, in which the late time acceleration of the Universe is determined by
the intrinsic geometry of the space-time.
