Teleparallel Equivalent of Lovelock Gravity

TL;DR

This paper develops a teleparallel formulation of Lovelock gravity, extending the teleparallel equivalent of general relativity to higher-dimensional theories involving torsion, which could have significant cosmological implications.

Contribution

It introduces the first construction of a teleparallel equivalent of Lovelock gravity, expanding the framework of torsion-based modified gravity theories.

Findings

Constructed the teleparallel equivalent of Lovelock gravity.

Reviewed teleparallel equivalents of general relativity and Gauss-Bonnet gravity.

Provided a formulation without imposing the Weitzenböck connection.

Abstract

There is a growing interest in modified gravity theories based on torsion, as these theories exhibit interesting cosmological implications. In this work, inspired by the teleparallel formulation of general relativity, we present its extension to Lovelock gravity known as the most natural extension of general relativity in higher-dimensional space-times. First, we review the teleparallel equivalent of general relativity and Gauss-Bonnet gravity, and then we construct the teleparallel equivalent of Lovelock gravity. In order to achieve this goal we use the vielbein and the connection without imposing the Weitzenb{\"o}ck connection. Then, we extract the teleparallel formulation of the theory by setting the curvature to null.