  We carry out a suite of cosmological simulations of modified action f(R)
models where cosmic acceleration arises from an alteration of gravity instead
of dark energy. These models introduce an extra scalar degree of freedom which
enhances the force of gravity below the inverse mass or Compton scale of the
scalar. The simulations exhibit the so-called chameleon mechanism, necessary
for satisfying local constraints on gravity, where this scale depends on
environment, in particular the depth of the local gravitational potential. We
find that the chameleon mechanism can substantially suppress the enhancement of
power spectrum in the non-linear regime if the background field value is
comparable to or smaller than the depth of the gravitational potentials of
typical structures. Nonetheless power spectrum enhancements at intermediate
scales remain at a measurable level for models even when the expansion history
is indistinguishable from a cosmological constant, cold dark matter model.
Simple scaling relations that take the linear power spectrum into a non-linear
spectrum fail to capture the modifications of f(R) due to the change in
collapsed structures, the chameleon mechanism, and the time evolution of the
modifications.
