  On cosmological scales, observations of the cluster abundance currently place
the strongest constraints on f(R) gravity. These constraints lie in the
large-field limit, where the modifications of general relativity can correctly
be modeled by setting the Compton wavelength of the scalar field to its
background value. These bounds are, however, at the verge of penetrating into a
regime, where the modifications become nonlinearly suppressed due to the
chameleon mechanism and cannot be described by this linearized approximation.
For future constraints based on observations subjected to cluster abundance, it
is therefore essential to consistently model the chameleon effect. We analyze
descriptions of the halo mass function in chameleon f(R) gravity using a mass-
and environment-dependent spherical collapse model in combination with
excursion set theory and phenomenological fits to N-body simulations in the
LCDM and f(R) gravity scenarios. Our halo mass functions consistently
incorporate the chameleon suppression and cosmological parameter dependencies,
improving upon previous formalisms and providing an important extension to
N-body simulations for the application in consistent tests of gravity with
observables sensitive to the abundance of clusters.
