Lovelock Gravity at the Crossroads of Palatini and Metric Formulations

Details Lovelock Gravity at the Crossroads of Palatini and Metric Formulations Lovelock Gravity at the Crossroads of Palatini and Metric Formulations

2007-05-14

arxiv.org/abs/0705.1879v3

Phys.Lett.B661:158-161,2008

Physics

High Energy Physics

High Energy Physics - Theory

Revtex, 4 pp, no figures; v3: Presentation improved, a reference added

Scientific paper

10.1016/j.physletb.2008.02.012

We consider extensions of the Einstein-Hilbert Lagrangian to a general functional of metric and Riemann curvature tensor. A given such Lagrangian describes two different theories depending on considering connection and metric (Palatini formulation), or only the metric (metric formulation) as independent dynamical degrees of freedom. Equivalence of the Palatini and metric formulations at the level of equations of motion, which as we will argue is a manifestation of the Equivalence Principle, is the physical criterion that restricts form of the Lagrangians of modified gravity theories. We prove that within the class of modified gravity theories we consider, only the Lovelock gravity satisfies this requirement.

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