The Weyl-Cartan Gauss-Bonnet gravity

TL;DR

This paper explores a generalized Gauss-Bonnet gravity in 4D Weyl-Cartan space-time, revealing new dynamics due to torsion and Weyl vectors, and reducing to a GR extension with vector fields.

Contribution

It introduces a novel 4D Weyl-Cartan Gauss-Bonnet gravity model that includes torsion and Weyl vectors, and analyzes its parameter space and reduction to known theories.

Findings

Higher derivatives can be eliminated with suitable parameters.

The model reduces to GR plus two vector fields in a special case.

Healthy parameter regions are identified in 5D parameter space.

Abstract

In this paper, we consider the generalized Gauss-Bonnet action in $4$-dimensional Weyl-Cartan space-time. In this space-time, the presence of torsion tensor and Weyl vector implies that the generalized Gauss-Bonnet action will not be a total derivative in four dimension space-time. It will be shown that the higher than two time derivatives can be removed from the action by choosing suitable set of parameters. In the special case where only the trace part of the torsion remains, the model reduces to GR plus two vector fields. One of which is massless and the other is massive. We will then obtain the healthy region of the 5-dimensional parameter space of the theory in some special cases.