Voids in Modified Gravity Reloaded: Eulerian Void Assignment
  We revisit the excursion set approach to calculate void abundances in
chameleon-type modified gravity theories, which was previously studied by
Clampitt, Cai and Li (2013). We focus on properly accounting for the
void-in-cloud effect, i.e., the growth of those voids sitting in over-dense
regions may be restricted by the evolution of their surroundings. This effect
may change the distribution function of voids hence affect predictions on the
differences between modified gravity and GR. We show that the thin-shell
approximation usually used to calculate the fifth force is qualitatively good
but quantitatively inaccurate. Therefore, it is necessary to numerically solve
the fifth force in both over-dense and under-dense regions. We then generalise
the Eulerian void assignment method of Paranjape, Lam and Sheth (2012) to our
modified gravity model. We implement this method in our Monte Carlo simulations
and compare its results with the original Lagrangian methods. We find that the
abundances of small voids are significantly reduced in both modified gravity
and GR due to the restriction of environments. However, the change in void
abundances for the range of void radii of interest for both models is similar.
Therefore, the difference between models remains similar to the results from
the Lagrangian method, especially if correlated steps of the random walks are
used. As Clampitt, Cai and Li (2013), we find that the void abundance is much
more sensitive to modified gravity than halo abundances. Our method can then be
a faster alternative to N-body simulations for studying the qualitative
behaviour of a broad class of theories. We also discuss the limitations and
other practical issues associated with its applications.
