Symmetric Teleparallel Gauss-Bonnet Gravity and its Extensions

TL;DR

This paper develops a differential form formulation of Gauss-Bonnet invariants within symmetric teleparallel gravity, introduces new scalar invariants, and constructs novel modified theories based on nonmetricity.

Contribution

It provides a new differential form approach to Gauss-Bonnet invariants in symmetric teleparallel gravity and introduces novel scalar invariants for modified theories.

Findings

Expressed Riemannian Gauss-Bonnet invariant in terms of teleparallel invariants.

Identified boundary terms and alternative splits in four dimensions.

Formulated new modified symmetric teleparallel theories using these scalars.

Abstract

General Teleparallel theories assume that curvature is vanishing in which case gravity can be solely represented by torsion and/or nonmetricity. Using differential form language, we express the Riemannian Gauss-Bonnet invariant concisely in terms of two General Teleparallel Gauss-Bonnet invariants, a bulk and a boundary one. Both terms are boundary terms in four dimensions. We also find that the split is not unique and present two possible alternatives. In the absence of nonmetricity our expressions coincide with the well-known Metric Teleparallel Gauss-Bonnet invariants for one of the splits. Next, we focus on the description where only nonmetricity is present and show some examples in different spacetimes. We finish our discussion by formulating novel modified Symmetric Teleparallel theories constructed with our new scalars.