We review the effects of modified gravity theories, in particular the symmetron and [Formula: see text] gravity, on the nonlinear regime of structure formation. In particular, we investigate the velocity dispersion of galaxy clusters as a function of the halo masses, how the matter power spectra depend on the coupling, range, and screening scale of the fifth force, and on possible ways of detecting violations of the equivalence principle using the mass inferred via lensing methods versus the mass inferred via dynamical methods. Furthermore, we show how one could use different voids statistics as one of the most promising probes of modified gravity.
Nonlinear Structure Formation, Backreaction and Weak Gravitational Fields
