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Paper   IPM / P / 8508
School of Physics
  Title:   Lovelock Gravity at the Crossroads of Palatini and Metric Formulations
1.  Q. Exirifard
2.  M.M. Sheikh-Jabbari
  Status:   Published
  Journal: Phys. Lett. B
  Vol.:  661
  Year:  2008
  Pages:   158-161
  Supported by:  IPM
We consider extension of the Einstein-Hilbert Lagrangian to a general function of metric and Riemann curvature tensor, L(gμν, Rμ  αβν). In these extension the metric and the connection could be thought as independent degrees of freedom (the Palatini formulation) or the connection could be replaced by Levi-Civita connection expressed in terms of derivative of metric (the metric formulation). For a general \cL the Palatini and metric formulations lead to different dynamical equations for gravity. In this letter we show that requiring the equivalence of the two formulations, at the level of equations of motion, severely restricts the possible forms of the Lagrangians. We show that the Lovelock gravity theories are the only theories of modified gravity which satisfy this criterion.

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