The Santiago-Harvard-Edinburgh-Durham void comparison I: SHEDding light
  on chameleon gravity tests
  We present a systematic comparison of several existing and new void finding
algorithms, focusing on their potential power to test a particular class of
modified gravity models - chameleon $f(R)$ gravity. These models deviate from
standard General Relativity (GR) more strongly in low-density regions and thus
voids are a promising venue to test them. We use Halo Occupation Distribution
(HOD) prescriptions to populate haloes with galaxies, and tune the HOD
parameters such that the galaxy two-point correlation functions are the same in
both f(R) and GR models. We identify both 3D voids as well as 2D underdensities
in the plane-of-the-sky to find the same void abundance and void galaxy number
density profiles across all models, which suggests that they do not contain
much information beyond galaxy clustering. However, the underlying void dark
matter density profiles are significantly different, with f(R) voids being more
underdense than GR ones, which leads to f(R) voids having a larger tangential
shear signal than their GR analogues. We investigate the potential of each void
finder to test f(R) models with near-future lensing surveys such as EUCLID and
LSST. The 2D voids have the largest power to probe f(R) gravity, with a LSST
analysis of tunnel (which is a new type of 2D underdensity introduced here)
lensing distinguishing at 80 and 11$\sigma$ (statistical error) f(R) models
with $|f_{R0}|=10^{-5}$ and $10^{-6}$ from GR.
