f(R) Gravity and Chameleon Theories (0806.3415v2)

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.

• The paper demonstrates that f(R) gravity models, with chameleon mechanisms, can hide scalar interactions to reproduce ΛCDM-like behavior.
• It rigorously applies experimental data, including Eöt-Wash tests, to constrain deviations from Newtonian gravity and enforce a dark energy equation near -1.
• The findings suggest that small-scale perturbative deviations may offer new avenues for testing gravity modifications in future cosmological investigations.

Exploration of $f(R)$ Gravity and Chameleon Theories in Cosmological and Experimental Contexts

This paper investigates the theoretical framework of $f(R)$ gravity and its potential role in explaining dark energy, primarily by analyzing its connections with chameleon theories. The authors rigorously explore $f(R)$ modifications of Einstein's gravity, focusing on their formulation as scalar-tensor theories and addressing the significant experimental challenges they face.

Theoretical Background and Motivation

The motivation for examining $f(R)$ gravity arises from the limitations of the standard cosmological model in explaining the acceleration of the universe's expansion. Two primary approaches exist: introducing a new form of matter, often referred to as dark energy, or modifying gravity itself. $f(R)$ gravity is a class of models that exemplifies the latter approach by replacing the Ricci scalar, $R$, in the action of General Relativity with a more general function $f(R)$.

The paper notes $f(R)$ theories inherently imply a strong coupling of the scalar field to matter, violating gravitational tests of Newton's law. To overcome this, chameleon theories, which allow for a matter-dependent mass and thin shell effects, offer a way to hide these scalar interactions in dense environments while allowing deviations in low-density cosmological settings.

Experimental and Cosmological Constraints

The analysis rigorously examines constraints arising from both experimental and cosmological observations, particularly the Eöt-Wash experiments. Despite the potential of $f(R)$ models, the paper concludes that the thin shell condition imposes severe restrictions on the cosmological dynamics, constraining the dark energy equation of state to values exceedingly close to $-1$ near the current epoch. This result suggests any observable deviation from a $\Lambda$CDM model at the background level of cosmology is unlikely.

The authors delineate the conditions necessary for an $f(R)$ theory to manifest chameleon-like behavior, which is essential for consistency with both cosmological evolution and laboratory constraints. They demonstrate that even with the existence of a thin shell, deviations from the inverse square law in experimental tests are not guaranteed to be null, potentially challenging the experimental viability of $f(R)$ models.

Implications and Future Directions

The paper emphasizes the importance of ensuring $f(R)$ gravity models can reconcile both cosmological observations and stringent laboratory tests. The findings underscore that while such models may reproduce the behavior of a $\Lambda$CDM cosmology at large scales, detectable deviations could emerge at smaller, perturbative levels due to anomalous growth in density contrast. This opens the possibility of future investigations and experiments focusing on these perturbative detections, thus offering a path for probing new physics in the context of cosmological structure formation.

In summary, this study provides a comprehensive examination of $f(R)$ gravity's viability as a dark energy model, highlighting critical constraints and pathways for theoretical consistency and experimental verification. Future work might focus on refining $f(R)$ models further to explore their implications on galaxy formation and small-scale cosmic structures, testing the bounds of current and upcoming observational capabilities.