Linear analysis of the gravitational beam–plasma instability

We investigate the well-known phenomenon of beam-plasma instability in gravitational sector, when a fast population particles interacts with massive scalar mode an Horndeski theory gravity, resulting into linear growth latter amplitude. Following approach used standard electromagnetic case, we start from dielectric representation plasma, as introduced previous analysis Landau damping for mode. Then, set up modified Vlasov-Einstein equation, using at first Dirac delta function to describe beam distribution. This way, provide analytical expression dispersion relation and demonstrate existence non-zero rate evolution A numerical investigation is then performed trapezoidal distribution function, which confirms results allows how decreases spread increases.