Limit to General Relativity in f(R) theories of gravity

TL;DR

This paper examines the behavior of f(R) gravity theories in the limit to General Relativity, analyzing scalar-tensor representations and spherically symmetric solutions, and concludes that f(R) models are unlikely to explain cosmic acceleration.

Contribution

It provides a detailed analysis of the scalar-tensor representation's behavior in the limit to GR and compares linearized solutions with existing literature, highlighting the impact of cosmic evolution.

Findings

Scalar-tensor representation remains well-behaved as f(R) approaches R

Linearized solutions are significantly influenced by cosmic evolution

Low-curvature f(R) models are unlikely to cause cosmic acceleration

Abstract

We discuss two aspects of f(R) theories of gravity in metric formalism. We first study the reasons to introduce a scalar-tensor representation for these theories and the behavior of this representation in the limit to General Relativity, f(R)--> R. We find that the scalar-tensor representation is well behaved even in this limit. Then we work out the exact equations for spherically symmetric sources using the original f(R) representation, solve the linearized equations, and compare our results with recent calculations of the literature. We observe that the linearized solutions are strongly affected by the cosmic evolution, which makes very unlikely that the cosmic speedup be due to f(R) models with correcting terms relevant at low curvatures.