Weyl-Cartan-Weitzenb\"{o}ck gravity as a generalization of teleparallel gravity

TL;DR

This paper introduces a gravitational model in Weyl-Cartan space-time with a Weitzenböck condition and torsion dynamics, exploring its cosmological implications including accelerated expansion and dark energy modeling.

Contribution

It generalizes teleparallel gravity by incorporating Weyl vector and torsion, deriving field equations, and analyzing cosmological solutions with diverse dynamic behaviors.

Findings

The model admits de Sitter late-time solutions.

It can describe accelerated cosmic expansion without dark energy.

Various cosmological evolutions are achievable depending on parameter choices.

Abstract

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.