Solar System constraints to general f(R) gravity

TL;DR

This paper investigates whether generalized $f(R)$ gravity can drive cosmic acceleration without contradicting Solar System tests. It develops a direct weak-field analysis in the metric formalism around a spherical mass, deriving a Klein–Gordon–like equation for the Ricci scalar perturbation and solving for the metric potentials. The key finding is that for broad classes with nonzero $f_{RR0}$ and a light scalar ($m^2 r^2 \ll 1$), the predicted PPN parameter is $\gamma=1/2$, in tension with observations, whereas in the GR limit ($f_{RR0}=0$) one recovers $\gamma=1$; case studies illustrate how models such as 1/R, Starobinsky, and hybrids behave under these constraints. Overall, the work places strong Solar System constraints on many $f(R)$ models, suggesting that viable cosmologies require either parameter regimes that suppress the scalar effects in the Solar System or additional screening mechanisms.

Abstract

It has been proposed that cosmic acceleration or inflation can be driven by replacing the Einstein-Hilbert action of general relativity with a function f(R) of the Ricci scalar R. Such f(R) gravity theories have been shown to be equivalent to scalar-tensor theories of gravity that are incompatible with Solar System tests of general relativity, as long as the scalar field propagates over Solar System scales. Specifically, the PPN parameter in the equivalent scalar-tensor theory is gamma=1/2, which is far outside the range allowed by observations. In response to a flurry of papers that questioned the equivalence of f(R) theory to scalar-tensor theories, it was recently shown explicitly, without resorting to the scalar-tensor equivalence, that the vacuum field equations for 1/R gravity around a spherically symmetric mass also yield gamma= 1/2. Here we generalize this analysis to f(R) gravity and enumerate the conditions that, when satisfied by the function f(R), lead to the prediction that gamma=1/2.