Post-Newtonian constraints on f(R) cosmologies in Palatini formalism

TL;DR

This paper derives constraints on f(R) gravity theories in the Palatini formalism using post-Newtonian limits, showing that viable models must be nearly linear in R and cannot explain cosmic acceleration.

Contribution

It provides explicit inequalities and bounds on the nonlinear terms of f(R) in the Palatini formalism based on observational tests.

Findings

f(R) must be nearly linear in R

Nonlinear corrections at low curvature are incompatible with experiments

Modified gravity cannot explain cosmic acceleration in this framework

Abstract

We compute the complete post-Newtonian limit of the Palatini form of f(R) gravities using a scalar-tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of inequalities that any lagrangian f(R) must satisfy. The constraints imposed by those inequalities allow us to find explicit functions that bound from above and from below the possible nonlinear terms of the lagrangian. We conclude that the lagrangian f(R) must be almost linear in R and that nonlinear corrections that grow at low curvatures are incompatible with observations. This result shows that modifications of gravity at very low cosmic densities cannot be responsible for the observed cosmic speed-up.