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We generalize the known equivalence between higher order gravity theories andscalar tensor theories to a new class of theories. Specifically, in the contextof a first order or Palatini variational principle where the metric andconnection are treated as independent variables, we consider theories for whichthe Lagrangian density is a function f of (i) the Ricci scalar computed fromthe metric, and (ii) a second Ricci scalar computed from the connection. Weshow that such theories can be written as tensor-multi-scalar theories with twoscalar fields with the following features: (i) the two dimensional sigma-modelmetric that defines the kinetic energy terms for the scalar fields hasconstant, negative curvature; (ii) the coupling function determining thecoupling to matter of the scalar fields is universal, independent of the choiceof function f; and (iii) if both mass eigenstates are long ranged, then theEddington post-Newtonian parameter has value 1/2. Therefore in order to becompatible with solar system experiments at least one of the mass eigenstatesmust be short ranged.Comment: 5 pages, no figures, revtex; references adde

Higher-order gravity theories and scalar–tensor theories