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

TL;DR

The paper investigates whether $f(R)$ gravity can explain cosmic acceleration while remaining consistent with local gravity tests. It maps $f(R)$ theories to Einstein gravity with a scalar field, then shows that the standard weak-field expansion often breaks down due to non-linearities; in high-curvature backgrounds, the Chameleon mechanism can suppress the scalar force and recover GR via thin-shell effects. In low-curvature models with $m_s\sim H_0$, linearized solutions resemble massless Brans–Dicke gravity and conflict with Solar System data unless non-perturbative effects intervene; in high-curvature regimes, the non-linear Chameleon dynamics typically restores GR, while certain fine-tuned or $R^2$-augmented models fail due to a breakdown of the mechanism or observational constraints. The results emphasize that viability of $f(R)$ models hinges on non-linear effects and the background curvature evolution, with potential GR-to-scalar-tensor transitions as the Universe evolves. Overall, non-perturbative Chameleon dynamics plays a crucial role in reconciling cosmic acceleration with local gravity tests, severely constraining the form of admissible $f(R)$ actions.

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.