  We study the linear and nonlinear structure formation in the dilaton and
symmetron models of modified gravity using a generic parameterisation which
describes a large class of scenarios using only a few parameters, such as the
coupling between the scalar field and the matter, and the range of the scalar
force on very large scales. For this we have modified the N-body simulation
code ECOSMOG, which is a variant of RAMSES working in modified gravity
scenarios, to perform a set of 110 simulations for different models and
parameter values, including the default LCDM. These simulations enable us to
explore a large portion of the parameter space. We have studied the effects of
modified gravity on the matter power spectrum and mass function, and found a
rich and interesting phenomenology where the difference with the LCDM template
cannot be reproduced by a linear analysis even on scales as large as k~0.05
h/Mpc. Our results show the full effect of screening on nonlinear structure
formation and the associated deviation from LCDM. We also investigate how
differences in the force mediated by the scalar field in modified gravity
models lead to qualitatively different features for the nonlinear power
spectrum and the halo mass function, and how varying the individual model
parameters changes these observables. The differences are particularly large in
the nonlinear power spectra whose shapes for f(R), dilaton and symmetron models
vary greatly, and where the characteristic bump around 1 h/Mpc of f(R) models
is preserved for symmetrons, whereas an increase on much smaller scales is
particular to symmetrons. No bump is present for dilatons where a flattening of
the power spectrum takes place on small scales. These deviations from LCDM and
the differences between modified gravity models, such as dilatons and
symmetrons, could be tested with future surveys.
