Cluster Constraints on f(R) Gravity

TL;DR

This work tests modified gravity in the form of $f(R)$ with cluster abundances, focusing on the Hu–Sawicki model and the parameter $|f_{R0}|$ that sets the strength and range of gravity modification via the Compton wavelength $\lambda_C$. Using simulation-calibrated mass-function enhancements derived from nonlinear structure formation and a Sheth–Tormen framework, the authors translate cluster counts in the $M_{500}$ regime into constraints on $|f_{R0}|$. By combining local cluster data with geometric probes from the CMB, supernovae, $H_0$, and BAO, they achieve an overall improvement of about $4$ orders of magnitude in the field amplitude and a $2$-order improvement in the range of the modification to gravity. The study demonstrates the power of cluster abundances as a nonlinear, model-agnostic probe of gravity and provides a robust path to constrain $f(R)$ theories in the context of cosmological data.

Abstract

Modified gravitational forces in models that seek to explain cosmic acceleration without dark energy typically predict deviations in the abundance of massive dark matter halos. We conduct the first, simulation calibrated, cluster abundance constraints on a modified gravity model, specifically the modified action f(R) model. The local cluster abundance, when combined with geometric and high redshift data from the cosmic microwave background, supernovae, H_0 and baryon acoustic oscillations, improve previous constraints by nearly 4 orders of magnitude in the field amplitude. These limits correspond to a 2 order of magnitude improvement in the bounds on the range of the force modification from the several Gpc scale to the tens of Mpc scale.

Figures (3)

• Figure 1: Mass function enhancement at $z=0$ with respect to $\Lambda$CDM as a function of $M=M_{500}$, measured in $f(R)$ simulations with $|f_{R0}|=10^{-4}$. Also shown is the range of spherical collapse predictions from halopaper. For the constraints, we conservatively use the lower limit of the shaded band (dashed line).
• Figure 2: Mass function enhancement for $|f_{R0}|=10^{-4}$ from the spherical collapse model (black, solid) as in Fig. \ref{['fig:dndmSim']}, and the corresponding enhancement when increasing the linear power spectrum normalization in $\Lambda$CDM. The vertical line indicates the pivot mass $M_{\rm eff}$ used to calculate the likelihood. The blue dashed line shows the enhancement for a rescaled normalization ($\sigma_8^{\rm eff}=\sigma_8 \times 1.066$) that matches the $f(R)$ enhancement at $M_{\rm eff}$.
• Figure 3: Cluster likelihood as function of primordial normalization (quantified by the linear power spectrum normalization $\sigma_8^{{\Lambda{\rm CDM}}}$ a $\Lambda$CDM model would give), for fixed values of $\Omega_m=0.258$, $h=0.716$, and $|f_{R0}|=10^{-4}$ in case of the $f(R)$ prediction. The red short-dashed line shows the likelihood calculated using the full $f(R)$ mass function enhancement, while the blue long-dashed line shows the $\Lambda$CDM likelihood obtained with the rescaled normalization, $\sigma_8^{\rm eff}$.