f(R) actions, cosmic acceleration and local tests of gravity

TL;DR

This paper analyzes spherically symmetric solutions in f(R) gravity theories, examining their compatibility with local gravity tests and the conditions under which they recover Einstein gravity or deviate due to the Chameleon mechanism.

Contribution

It clarifies the validity of the weak field expansion in f(R) models and assesses the viability of models addressing Dark Energy with respect to local gravity constraints.

Findings

Weak field expansion often invalid in Dark Energy f(R) models

Chameleon mechanism enables Einstein gravity recovery at high background curvature

Certain dynamical Dark Energy models with large scalar mass are not viable

Abstract

We study spherically symmetric solutions in f(R) theories and its compatibility with local tests of gravity. We start by clarifying the range of validity of the weak field expansion and show that for many models proposed to address the Dark Energy problem this expansion breaks down in realistic situations. This invalidates the conclusions of several papers that make inappropriate use of this expansion. For the stable models that modify gravity only at small curvatures we find that when the asymptotic background curvature is large we approximately recover the solutions of Einstein gravity through the so-called Chameleon mechanism, as a result of the non-linear dynamics of the extra scalar degree of freedom contained in the metric. In these models one would observe a transition from Einstein to scalar-tensor gravity as the Universe expands and the background curvature diminishes. Assuming an adiabatic evolution we estimate the redshift at which this transition would take place for a source with given mass and radius. We also show that models of dynamical Dark Energy claimed to be compatible with tests of gravity because the mass of the scalar is large in vacuum (e.g. those that also include R^2 corrections in the action), are not viable.