Testing $f(R)$ Gravity With Scale Dependent Cosmic Void Velocity Profiles

We study the impact of cosmological scale modifications to General Relativity on the dynamics of halos within voids by comparing N-body simulations incorporating Hu-Sawicki $f(R)$ gravity, with $|f_{R0}|=10^{-6}$ and $10^{-5}$, to those of $\Lambda$CDM. By examining the radial velocity statistics within voids classified based on their size and density-profile, as "rising" ($R$-type) or "shell" ($S$-type), we find that halo motions in small $R$-type voids, with effective radius $<15 Mpc/h$, reveal distinctive differences between $f(R)$ and $\Lambda$CDM cosmologies. To understand this observed effect, we study the linear and nonlinear fifth forces, and develop an iterative algorithm to accurately solve the non-linear fifth force equation. We use this to characterize the Chameleon screening mechanism in voids and contrast the behavior with that observed in gravitationally collapsed objects. The force analysis underscores how smaller $R$-type voids exhibit the highest ratios of fifth force to Newtonian force, which source distinguishable differences in the velocity profiles and thereby provide rich environments in which to constrain gravity.