f(R) Gravity and Chameleon Theories

TL;DR

This work analyzes f(R) gravity as a dark-energy candidate by exploiting its scalar-tensor equivalence and the chameleon screening mechanism. By enforcing thin-shell screening and lab-based inverse-square-law tests (notably the Eöt-Wash experiment), the authors derive stringent bounds on the scalar field and the form of f(R), demonstrating that viable models must remain extremely close to Lambda-CDM at the background level ($|1+w_{\rm eff}|\Omega_{\rm de}^{\rm eff} \lesssim 10^{-4}$ in the recent past). They examine specific model classes, including logarithmic and power-law potentials, showing that logarithmic models are ruled out by local tests while certain power-law forms survive the constraints but with tight parameter restrictions. Overall, the paper concludes that cosmological and laboratory tests jointly favor f(R) models that are practically indistinguishable from $\Lambda$CDM on background evolution, with potential subtle signatures emerging only at perturbative or sub-galactic scales.

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.

Figures (2)

• Figure 1: Eöt-Wash constraints (thick solid blue line) on $f(R)$ gravity theories with $f(R) = R + h(R)$ where $h(R) = \bar{R} (R/\bar{R})^{p+1}$; $\bar{R}=\Lambda_0^4/M_{\rm Pl}^2$ and $-5 < p < -1$, $-1 < p < 0$ and $0 < p < 1$. For this constraint we have assumed that the test bodies have thin-shells (which is necessary to avoid local tests). We have also shown : (1) the cosmological thin shell constraint (thick red dashed line) for test bodies in the laboratory derived in Section \ref{['sec:cosmo']}, (2) the naive constraint (thick black dotted line) one could derive by simply requiring that, inside the test bodies, the mass of the chameleon at the minimum of its effective potential, $m_c$is large compared with the length scale of the body, $D_{p}$. This was the constraint considered in Ref. Staro. For all such theories we see that the correctly evaluated constraint provided by the Eöt-Wash experiment EotWash is stronger than both this naïve constraint and the cosmological thin-shell bound for all for $p \gtrsim -1$. The $m_c D_{\rm p} \gg 1$ constraint never provides the strongest constraint.
• Figure 2: Combined Eöt-Wash constraints on the effective dark energy equation of state parameter produced by $f(R)$ gravity theories with $f(R) = R + h(R)$ where $h(R) = \bar{R} (R/\bar{R})^{p+1}$. $\bar{R}=\Lambda_0^4/M_{\rm Pl}^2$ and $-5 < p < -1$, $-1 < p < 0$ and $0 < p < 1$. These constraints have been derived by requiring both that the Eöt-Wash test masses have thin-shells and by requiring that the chameleonic torque produced between the two thin-shelled test masses is small enough to have avoided detection to date. We see that in all cases we have $\vert 1 + w_{\rm de}^{\rm eff}\vert < 10^{-4}$ today. As a result, the late time cosmology of any viable theory would be virtually indistinguishable from that described by the $\Lambda$CDM model