An Extended Excursion Set Approach to Structure Formation in Chameleon
  Models
  In attempts to explain dark energy, a number of models have been proposed in
which the formation of large-scale structure depends on the local environment.
These models are highly non-linear and difficult to analyse analytically.
N-body simulations have therefore been used to study their non-linear
evolution. Here we extend excursion set theory to incorporate environmental
effects on structure formation. We apply the method to a chameleon model and
calculate observables such as the non-linear mass function at various
redshifts. The method can be generalized to study other obervables and other
models of environmentally dependent interactions. The analytic methods
described here should prove useful in delineating which models deserve more
detailed study with N-body simulations.
