Higher order gravity theories and scalar tensor theories

Abstract

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.

5 pages, no figures, revtex; references added

References in corpus (6)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Can the dark energy equation-of-state parameter w be less than -1?
• The Confrontation between General Relativity and Experiment
• Extended Gravity Theories and the Einstein-Hilbert Action
• Comparing selfinteracting scalar fields and R + R^3 cosmological models

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