Gauss-Bonnet lagrangian G ln G and cosmological exact solutions

Abstract

For the lagrangian L = G ln G where G is the Gauss-Bonnet curvature scalar we deduce the field equation and solve it in closed form for 3-flat Friedman models using a statefinder parametrization. Further we show, that among all lagrangians F(G) this L is the only one not having the form G^r with a real constant r but possessing a scale-invariant field equation. This turns out to be one of its analogies to f(R)-theories in 2-dimensional space-time. In the appendix, we systematically list several formulas for the decomposition of the Riemann tensor in arbitrary dimensions n, which are applied in the main deduction for n=4.

18 pages, amended version, accepted by Phys. Rev. D

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Cited by in corpus (8)

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• Effects of $f(R,G)$ gravity on anisotropic charged compact objects
• Cosmography in F(G) modified gravity
• Energy Conditions in Extended $f(R,G,T)$ Gravity
• Modified Einstein-Gauss-Bonnet gravity: Riemann-Cartan and Pseudo-Riemannian cases