Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-09-03
Class.Quant.Grav. 21 (2003) 417-426
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
5 pages, no figures, revtex; references added
Scientific paper
10.1088/0264-9381/21/2/006
We generalize the known equivalence between higher order gravity theories and scalar tensor theories to a new class of theories. Specifically, in the context of a first order or Palatini variational principle where the metric and connection are treated as independent variables, we consider theories for which the Lagrangian density is a function f of (i) the Ricci scalar computed from the metric, and (ii) a second Ricci scalar computed from the connection. We show that such theories can be written as tensor-multi-scalar theories with two scalar fields with the following features: (i) the two dimensional sigma-model metric that defines the kinetic energy terms for the scalar fields has constant, negative curvature; (ii) the coupling function determining the coupling to matter of the scalar fields is universal, independent of the choice of function f; and (iii) if both mass eigenstates are long ranged, then the Eddington post-Newtonian parameter has value 1/2. Therefore in order to be compatible with solar system experiments at least one of the mass eigenstates must be short ranged.
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