Palatini form of 1/R gravity

Abstract

It has been suggested that the recent acceleration of the expansion of the Universe is due a modified gravitational action consisting of the Einstein-Hilbert term plus a term proportional to the reciprocal of the Ricci scalar. Although the original version of this theory has been shown to be in conflict with solar system observations, a modified Palatini version of the theory, in which the metric and connection are treated as independent variables in the variational principle, has been suggested as a viable model of the cosmic acceleration. We show that this theory is equivalent to a type of scalar-tensor theory in which the scalar field kinetic energy term in absent from the action, and in which the scalar field is therefore not an independent dynamical degree of freedom. Integrating out the scalar field gives rise to additional interactions among the matter fields of the standard model of particle physics at a energy scale of order 10^(-3) eV (the geometric mean of the Hubble scale and the Planck scale), and so the theory is excluded by, for example, electron-electron scattering experiments.