Gauss-Bonnet Lagrangian G ln G and cosmological exact solutions
- 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.
Author details: | Hans-Jürgen Schmidt |
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URL: | http://arxiv.org/pdf/1102.0241v2 |
ISSN: | 1550-7998 |
Publication type: | Article |
Language: | English |
Year of first publication: | 2011 |
Publication year: | 2011 |
Release date: | 2017/03/25 |
Source: | Physical Review D. - ISSN 1550-7998. - 83 (2011), 8, 083513 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |