Dynamical analysis of screening in scalar-tensor theory

We investigate linear and nonlinear dynamics of spherically symmetric perturbations on a static configuration in scalar-tensor theories focusing the chameleon screening mechanism. particularly address two questions: how much can source fifth force when background is well screened, whether resultant change stability structure configuration. For perturbations, we derive lower bound for square Fourier mode frequency ${\ensuremath{\omega}}^{2}$ using adiabatic approximation. There may be unstable modes if this negative, find that condition instability changed by although effect suppressed parameter. because are mainly interested short wavelength which become stronger, perform numerical simulations under planar sufficiently large initial amplitude density perturbation, magnitude comparable to Newtonian gravity even model parameters chosen so screened. It also shown effective background, fluid mostly governed pressure gradient not significantly affected force.