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

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.

17 pages

References in corpus (14)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy
• The Cosmology of Modified Gauss-Bonnet Gravity
• Cosmology and Astrophysical Constraints of Gauss-Bonnet Dark Energy
• Gauss-Bonnet Quintessence: Background Evolution, Large Scale Structure and Cosmological Constraints
• Accelerating cosmologies from non-local higher-derivative gravity
• Cosmological applications of $F(T,T_G)$ gravity
• Accelerating Cosmologies in the Einstein-Gauss-Bonnet Theory with Dilaton
• Post-Newtonian expansion for Gauss-Bonnet Gravity
• Einstein-Cartan Theory
• Some exact solutions with torsion in 5-D Einstein-Gauss-Bonnet gravity
• Gauss-Bonnet lagrangian G ln G and cosmological exact solutions
• Solar System Constraints on f(G) Dark Energy

Cited by in corpus (2)

• Pre-geometric Einstein-Cartan Field Equations and Emergent Cosmology
• Inflation with the Gauss-Bonnet term in the Palatini formulation