f(R) Gravity and Chameleon Theories

TL;DR

This paper investigates f(R) gravity models as dark energy candidates, analyzing their connection to chameleon theories, and finds that observational constraints tightly restrict these models to behave very similarly to the standard Lambda-CDM cosmology.

Contribution

It provides a detailed analysis of f(R) theories' compatibility with experimental tests and cosmological observations, highlighting the constraints on their deviations from Lambda-CDM.

Findings

f(R) models must have an equation of state close to -1

Thin shell effects limit deviations from Newton's law

Cosmological and laboratory tests strongly constrain f(R) models

Abstract

We analyse f(R) modifications of Einstein's gravity as dark energy models in the light of their connection with chameleon theories. Formulated as scalar-tensor theories, the f(R) theories imply the existence of a strong coupling of the scalar field to matter. This would violate all experimental gravitational tests on deviations from Newton's law. Fortunately, the existence of a matter dependent mass and a thin shell effect allows one to alleviate these constraints. The thin shell condition also implies strong restrictions on the cosmological dynamics of the f(R) theories. As a consequence, we find that the equation of state of dark energy is constrained to be extremely close to -1 in the recent past. We also examine the potential effects of f(R) theories in the context of the Eot-wash experiments. We show that the requirement of a thin shell for the test bodies is not enough to guarantee a null result on deviations from Newton's law. As long as dark energy accounts for a sizeable fraction of the total energy density of the Universe, the constraints which we deduce also forbid any measurable deviation of the dark energy equation of state from -1. All in all, we find that both cosmological and laboratory tests imply that f(R) models are almost coincident with a Lambda-CDM model at the background level.