Testing Gravity using Void Profiles
  We investigate void properties in $f(R)$ models using N-body simulations,
focusing on their differences from General Relativity (GR) and their
detectability. In the Hu-Sawicki $f(R)$ modified gravity (MG) models, the halo
number density profiles of voids are not distinguishable from GR. In contrast,
the same $f(R)$ voids are more empty of dark matter, and their profiles are
steeper. This can in principle be observed by weak gravitational lensing of
voids, for which the combination of a spectroscopic redshift and a lensing
photometric redshift survey over the same sky is required. Neglecting the
lensing shape noise, the $f(R)$ model parameter amplitudes $|f_{R0}|=10^{-5}$
and $10^{-4}$ may be distinguished from GR using the lensing tangential shear
signal around voids by 4 and 8$\sigma$ for a volume of 1~(Gpc/$h$)$^3$. The
line-of-sight projection of large-scale structure is the main systematics that
limits the significance of this signal for the near future wide angle and deep
lensing surveys. For this reason, it is challenging to distinguish
$|f_{R0}|=10^{-6}$ from GR. We expect that this can be overcome with larger
volume. 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 $\sigma_8$.
