Modified Einstein-Gauss-Bonnet gravity: Riemann-Cartan and Pseudo-Riemannian cases

TL;DR

This paper explores a modified Einstein-Gauss-Bonnet gravity model in four dimensions, analyzing both Riemannian and non-Riemannian cases, deriving field equations, and demonstrating the existence of de-Sitter solutions with scalar fields.

Contribution

It introduces a unified variational approach for both pseudo-Riemannian and non-Riemannian geometries in modified gravity with Gauss-Bonnet terms, including perturbative treatment of torsion.

Findings

Existence of maximally symmetric de-Sitter solutions with scalar fields in both cases

Derivation of field equations using constrained-first order formalism

Perturbative scheme for non-Riemannian case with torsion

Abstract

A modified Einstein-Gauss-Bonnet gravity in four dimensions where the quadratic Gauss-Bonnet term is coupled to a scalar field is considered. The field equations of the model are obtained by variational methods by making use of the constrained-first order formalism covering both pseudo-Riemannian and non-Riemannian cases. In the pseudo-Riemannian case, the Lagrange multiplier forms, which impose the vanishing torsion constraint, are eliminated in favor of the remaining fields and the resulting metric field equations are expressed in terms of the double-dual curvature 2-form. In the non-Riemannian case with torsion, the field equations are expressed in terms of the pseudo-Riemannian quantities by a perturbative scheme valid for a weak coupling constant. It is shown that, for both cases, the model admits a maximally symmetric de-Sitter solution with nontrivial scalar field. Minimal coupling of a Dirac spinor to the Gauss-Bonnet modified gravity is also discussed briefly.