Bi-Connected Gauss-Bonnet Gravity

TL;DR

This paper introduces a bi-connection gravity model with Gauss-Bonnet terms, resolving previous dynamical issues and revealing self-accelerating solutions, with potential links to massive gravity theories.

Contribution

It extends bi-connection models by incorporating Gauss-Bonnet terms, providing a consistent dynamical framework and exploring connections to massive gravity.

Findings

Self-accelerating solutions in Weyl-inspired bi-connection models

Automatic emergence of mixing terms between potential and kinetic parts

Resolution of dynamics issues in pure Einstein-Hilbert bi-connection models

Abstract

We consider a bi-connection model in the presence of four-dimensional Gauss-Bonnet term adding to the Einstein-Hilbert action. This generalization solves the dynamics issue which exists in pure Einstein-Hilbert formalism of bi-connection model. As an example we study the Weyl inspired bi-connection model and show there is a self-accelerating solution in this model. To compare it with previous results we try to find appropriate generalization of the Weyl geometrical bi-connection model to reach at de Rham-Gabadadze-Tolley massive gravity. In this formalism mixing terms between the potential and kinetic terms appear automatically.