Modified teleparallel theories of gravity -- Gauss-Bonnet and trace extensions

TL;DR

This paper explores extended teleparallel gravity theories incorporating Gauss-Bonnet terms and trace couplings, clarifying their relationships and identifying new models for future research.

Contribution

It formulates the teleparallel equivalent of Gauss-Bonnet gravity and uncovers novel modified gravity models within this framework.

Findings

Formulated the teleparallel equivalent of Gauss-Bonnet gravity.

Clarified connections between teleparallel and metric theories.

Identified new modified gravity models for further study.

Abstract

We investigate modified theories of gravity in the context of teleparallel geometries with possible Gauss-Bonnet contributions. The possible coupling of gravity with the trace of the energy-momentum tensor is also taken into account. This is motivated by the various different theories formulated in the teleparallel approach and the metric approach without discussing the exact relationship between them. Our formulation clarifies the connections between different well known theories. For instance, we are able to formulate the correct teleparallel equivalent of Gauss-Bonnet modified general relativity, amongst other results. Finally, we are able to identify modified gravity models which have not been studied in the past. These appear naturally within our setup and would make a interesting starting point for further studies.