Instability in classical and modified gravity

Gravitational instability in classical Jeans theory, General Relativity, and modified gravity is considered. A simple suggestion to eliminate the problem with zero order approximation in the Jeans theory is proposed. It is shown that density perturbations in the background with an increasing density rise faster than in the standard case of time independent background. Evolution of density and metric perturbations in the background of high frequency oscillations of curvature in F(R) gravity is studied. In addition to the usual Jeans-like instability new effects of amplification of perturbations, associated with parametric resonance and antifriction phenomena, are found.