Testing Gravity using Cosmic Voids
  We explore voids in dark matter and halo fields from simulations of
$\Lambda$CDM and Hu-Sawicki $f(R)$ models. In $f(R)$ gravity, dark matter void
abundances are greater than that of general relativity (GR). However, when
using haloes to identify voids, the differences of void abundances become much
smaller, but can still be told apart, in principle, at the 2, 6 and 14 $\sigma$
level for the $f(R)$ model parameter amplitudes of $|f_{R0}|=10^{-6}$,
$10^{-5}$ and $10^{-4}$. In contrast, the abundance of large voids found using
haloes in $f(R)$ gravity is lower than in GR. The more efficient halo formation
in underdense regions makes $f(R)$ voids less empty of haloes. This counter
intuitive result suggests that voids are not necessarily emptier in $f(R)$ if
one looks at galaxies in voids. Indeed, the halo number density profiles of
voids are not distinguishable from GR. However, the same $f(R)$ voids are more
empty of dark matter. This can in principle be observed by weak gravitational
lensing of voids, for which the combination of a spec-$z$ and a photo-$z$
survey over the same sky is necessary. For a volume of 1~(Gpc/$h$)$^3$,
neglecting the lensing shape noise, $|f_{R0}|=10^{-5}$ and $10^{-4}$ may be
distinguished from GR using the lensing tangential shear signal around voids by
4 and 8$\sigma$. The line-of-sight projection of large-scale structure is the
main systematics that limits the significance of this signal, limiting the
constraining power for $|f_{R0}|=10^{-6}$. The halo void abundance being
smaller and the steepening of dark matter void profiles in $f(R)$ models are
unique features that can be combined to break the degeneracy between $|f_{R0}|$
and $\sigma_8$. The outflow of mass from void centers and velocity dispersions
are greater in $f(R)$. Model differences in velocity profiles imply potential
powerful constraints of the model in phase space and in redshift space.
