[Paper Review] Chameleon $f(R)$ gravity on the Virgo cluster scale

C. Corbett Moran, Romain Teyssier+1 more|arXiv (Cornell University)|Aug 12, 2014

Galaxies: Formation, Evolution, Phenomena4 citations

TL;DR

This study performs the highest-resolution N-body zoom simulations to date of $f(R)$ gravity using the Hu-Sawicki chameleon model, showing that velocity dispersion and lensing profiles in Virgo-like clusters can distinguish $f(R)$ models from $\Lambda$CDM. Key results include robust detectability of modified gravity effects in satellite populations at low redshift, especially for F4 and F5 models, with environmental screening effects most pronounced at large radii and for poorly resolved subhalos.

ABSTRACT

Models of modified gravity offer promising alternatives to the concordance $Λ$CDM cosmology to explain the late-time acceleration of the universe. A popular such model is $f(R)$ gravity, in which the Ricci scalar in the Einstein-Hilbert action is replaced by a general function of it. We study the $f(R)$ model of Hu & Sawicki (2007), which recovers standard General Relativity in high density regimes, while reproducing the desired late-time acceleration at cosmological scales. We run a suite of high resolution zoom simulations using the ECOSMOG code to examine the effect of $f(R)$ gravity on the properties of a halo that is analogous to the Virgo cluster. We show that the velocity dispersion profiles can potentially discriminate between $f(R)$ models and $Λ$CDM, and provide complementary analysis of lensing signal profiles to explore the possibility to further distinguish the different $f(R)$ models. Our results confirm the techniques explored by Cabre et al. (2012) to quantify the effect of environment in the behavior of $f(R)$ gravity, and we extend them to study halo satellites at various redshifts. We find that the modified gravity effects in our models are most observable at low redshifts, and that effects are generally stronger for satellites far from the center of the main halo. We show that the screening properties of halo satellites trace very well that of dark matter particles, which means that low-resolution simulations in which subhalos are not very well resolved can in principle be used to study satellite properties. We discuss observables, particularly for halo satellites, that can potentially be used to constrain the observational viability of $f(R)$ gravity.

Motivation & Objective

• To investigate the viability of chameleon $f(R)$ gravity on cluster scales using high-resolution simulations.
• To test whether observable properties like velocity dispersion and lensing signals can distinguish $f(R)$ models from $\Lambda$CDM.
• To examine the environmental dependence of screening mechanisms on halo satellites across redshifts.
• To assess the reliability of proxies such as $|\phi_{\rm{ext}}|$ and $D_{11}$ for predicting screening in subhalos.
• To determine the conditions under which weak $f(R)$ models (e.g., F6) remain observationally distinguishable from $\Lambda$CDM.

Proposed method

• Performed high-resolution N-body zoom simulations using the ECOSMOG code to model a Virgo-like halo in the Hu-Sawicki $f(R)$ gravity model.
• Tracked the evolution of surface density and line-of-sight velocity dispersion profiles across multiple redshifts and $f(R)$ model parameters (F4, F5, F6).
• Computed lensing signal profiles to compare $f(R)$ gravity predictions with $\Lambda$CDM and assess observational discriminability.
• Defined and analyzed the screening parameter $\Delta_M$ and environmental proxies $|\phi_{\rm{ext}}|$ and $D_{11}$ to quantify fifth-force effects on satellites.
• Used the chameleon mechanism to model how scalar field screening suppresses fifth forces in high-density regions like cluster cores.
• Analyzed the transition from screened to unscreened regimes by comparing halo potential depth to the background $f_R$ value at each redshift.

Experimental results

Research questions

• RQ1 Can velocity dispersion profiles in Virgo-like clusters robustly distinguish $f(R)$ gravity models from $\Lambda$CDM?
• RQ2 How do lensing signal profiles in $f(R)$ gravity differ from those in $\Lambda$CDM, and can they be used to constrain model parameters?
• RQ3 What is the environmental dependence of screening on satellite galaxies, and how does it vary with redshift?
• RQ4 Can observables like $|\phi_{\rm{ext}}|$ reliably predict the screening state of satellite galaxies in $f(R)$ gravity?
• RQ5 To what extent are weak $f(R)$ models (e.g., F6) observationally distinguishable from $\Lambda$CDM, especially at low redshift?

Key findings

• The velocity dispersion profiles of F4 and F5 $f(R)$ models are robustly distinguishable from $\Lambda$CDM and the F6 model, especially at high redshift.
• Lensing signal profiles provide complementary discrimination, enabling distinction between F4 and F5 models at intermediate redshifts.
• A characteristic radius exists at each redshift beyond which chameleon screening fails, and this radius shrinks with time in all models.
• Particles outside of halos are generally unscreened across all models and redshifts, indicating strong fifth-force effects in low-density environments.
• Satellite galaxies at large radii from the main halo show enhanced fifth-force effects in weak $f(R)$ models (e.g., F6), with effects increasing toward the outer regions.
• The observable $|\phi_{\rm{ext}}|$ serves as a reliable proxy for the screening state of satellites, while the $D_{11}$ neighbor criterion is less effective for subhalos.