Excursion set theory for modified gravity: Eulerian versus Lagrangian
  environments
  We have revisited the extended excursion set theory in modified gravity
models, taking the chameleon model as an example. Instead of specifying their
Lagrangian size, here we define the environments by the Eulerian size, chosen
to be of the same order of the Compton length of the scalar field by physical
arguments. We find that the Eulerian and Lagrangian environments have very
different environmental density contrast probability distributions, the former
more likely to have high matter density, which in turn suppressing the effect
of the fifth force in matter clustering and halo formation. The use of Eulerian
environments also evades the unphysical restriction of having an upper mass
limit in the case of Lagrangian environments.Two methods of computing the
unconditional mass functions, numerical integration and Monte Carlo simulation,
are discussed and found to give consistent predictions.
