Constraining f(R) Gravity as a Scalar Tensor Theory

TL;DR

This work analyzes the viability of $f(R)$ gravity by exploiting its exact equivalence to scalar-tensor theories, focusing on solar-system constraints and cosmological implications. It identifies two robust pathways—Chameleon screening and large scalar mass—that allow $f(R)$ models to evade local tests, but finds that both lead to late-time acceleration that is observationally indistinguishable from a cosmological constant $\Lambda$. The authors further explore $f(R)$ inflation in polynomial models and derive constraints from fifth forces, BBN, density-dependent effects, and gravitational waves, showing that non-Λ dark energy is highly constrained and often unattainable within these frameworks. Collectively, the results suggest GR with $\Lambda$ remains remarkably consistent with data, and simple $f(R)$ constructions are unlikely to yield significantly distinct late-time cosmology, though they may inform high-energy and local-gravity phenomenology.

Abstract

We search for viable f(R) theories of gravity, making use of the equivalence between such theories and scalar-tensor gravity. We find that models can be made consistent with solar system constraints either by giving the scalar a high mass or by exploiting the so-called chameleon effect. However, in both cases, it appears likely that any late-time cosmic acceleration will be observationally indistinguishable from acceleration caused by a cosmological constant. We also explore further observational constraints from, e.g., big bang nucleosynthesis and inflation.

Figures (5)

• Figure 1: Effective potential for the Chameleon model Eq. (\ref{['eq:expansion']}) with decreasing $\bar{\rho}_{\rm{NR}}/\mu^2 M_{\rm{pl}}^2 = 100,50,20$ and $m=1$. Note that $\phi_{\rm{min}}$ and the mass $m_\phi^2$ (the curvature of the minimum) are very sensitive to the background energy density $\bar{\rho_{\rm NR}}$.
• Figure 2: Solar system constraints on the $f(R)$ Chameleon are seen to exclude all models where the "dark energy" is observationally distinguishable from a cosmological constant (labeled "dynamic DE"). The two different solar system constraint curves come from Eq. (\ref{['eq:sol']}) and Eq. (\ref{['eq:ssconstraints']}). Although it is not clear from the plot, the limits $m\rightarrow 0$, $m\rightarrow1$ and $\mu \rightarrow 0$ are all acceptable and yet give no dynamical DE. Indeed these are exactly the limits in which we recover standard GR.
• Figure 3: Potential for the $f(R)$ model in Eq. (\ref{['eq:polymodel']}) with various values of $\lambda$. Notice how the $\lambda=0$ case has an asymptotically flat potential as $\phi\rightarrow\infty$.
• Figure 4: Constraints on the cubic $f(R)$ model. The thin blue/grey sliver correspond to observationally allowed $f(R)$ inflationary scenarios. Shaded are regions we may rule out given a measurement of the tensor to scalar ratio $r$ and the assumption that they were generated by a period of slow roll inflation in the early universe. The $r=0.05$ and $r=0.01$ are the most realistic curve, in the sense that future experiments are sensitive to such values as low as $r=0.01$Bock:2006yf.
• Figure 5: Effective potential for the polynomial model Eq. (\ref{['eq:polymodel']}), with various JF inflationary energy densities $u(\psi)$, here $\lambda=0.1$.