Constraints on f(R) gravity from probing the large-scale structure

TL;DR

This work tests metric $f(R)$ gravity models that reproduce the $ ext{LCDM}$ expansion by introducing a single low-redshift parameter $B_0$ that encodes deviations from general relativity. Using a comprehensive MCMC analysis that combines CMB, SN, BAO, $H_0$, ISW, gISW, $E_G$, and cluster-abundance data within the PPF formalism, the authors quantify how growth of structure constrains the modified gravity sector. The strongest constraint arises from cluster abundances, yielding $B_0<1.12 imes10^{-3}$ (95% C.L.), with gISW and $E_G$ offering complementary improvements and CCCP data further tightening to $B_0<0.96 imes10^{-3}$ when included. The results demonstrate that current cosmological data impose stringent limits on infrared modifications to gravity, consistent with GR in high-curvature regimes, and highlight the continued promise of ISW-based probes and lensing–velocity correlations for future tests of gravity. These constraints inform the viability of $f(R)$ models and the role of the chameleon mechanism in screening modified forces in massive halos.

Abstract

We study cosmological constraints on metric f(R) gravity models that are designed to reproduce the LCDM expansion history with modifications to gravity described by a supplementary cosmological freedom, the Compton wavelength parameter B_0. We conduct a Markov chain Monte Carlo analysis on the parameter space, utilizing the geometrical constraints from supernovae distances, the baryon acoustic oscillation distances, and the Hubble constant, along with all of the cosmic microwave background data, including the largest scales, its correlation with galaxies, and a probe of the relation between weak gravitational lensing and galaxy flows. The strongest constraints, however, are obtained through the inclusion of data from cluster abundance. Using all of the data, we infer a bound of B_0<0.0011 at the 95% C.L.

Figures (6)

• Figure 1: Best-fit CMB temperature anisotropy power spectrum for $\Lambda$CDM and $f(R)$ gravity from using the Union, SHOES, BAO, and CMB data.
• Figure 2: Best-fit $\Lambda$CDM ($B_0=0$) gISW cross correlations (blue solid line) for the different galaxy samples, roughly ordered in increasing effective, bias-weighted, redshift. Adding nonzero values for the Compton wavelength parameter (red dashed lines): $B_0=0.1$ (top) and $B_0=0.5$ (bottom).
• Figure 3: Product of the linear density growth rate $D$ and the derivative of the linear potential growth rate $G$ with respect to redshift $z$. Solid lines are derived from linear perturbation theory, dashed lines are obtained through the approximation described in Sec. \ref{['gISW']}, using $h=0.73$ and $\Omega_{\rm m} = 0.24$. Note that $H_0 \simeq 3\times10^{-4}h~\textrm{Mpc}^{-1}$.
• Figure 4: Best-fit $\Lambda$CDM ($B_0=0$) $E_G$ prediction from linear theory (blue solid line). Left panel: adding nonzero values for the Compton wavelength parameter (red dashed lines): $B_0=1$ (top) and $B_0=0.1$ (bottom). Right panel: $E_G$ at different values of $B_0$, evaluated at $k=0.1h~\textrm{Mpc}^{-1}$.
• Figure 5: Marginalized likelihood for $B_0$ when using WMAP5, ACBAR, CBI, VSA, Union, SHOES, and BAO in combination with the additional data sets. For gISW, the Compton wavelength parameter is rescaled as $B_0\rightarrow 10^{-2}B_0$, i.e., the constraint is a factor of $10^2$ weaker than illustrated. The horizontal lines indicate 68%, 95%, and 99% confidence levels.