  As one of the most powerful probes of cosmological structure formation, the
abundance of massive galaxy clusters is a sensitive probe of modifications to
gravity on cosmological scales. In this paper, we present results from N-body
simulations of a general class of f(R) models, which self-consistently solve
the non-linear field equation for the enhanced forces. Within this class we
vary the amplitude of the field, which controls the range of the enhanced
gravitational forces, both at the present epoch and as a function of redshift.
Most models in the literature can be mapped onto the parameter space of this
class. Focusing on the abundance of massive dark matter halos, we compare the
simulation results to a simple spherical collapse model. Current constraints
lie in the large-field regime, where the chameleon mechanism is not important.
In this regime, the spherical collapse model works equally well for a wide
range of models and can serve as a model-independent tool for placing
constraints on f(R) gravity from cluster abundance. Using these results, we
show how constraints from the observed local abundance of X-ray clusters on a
specific f(R) model can be mapped onto other members of this general class of
models.

Cosmology and Nongalactic Astrophysics