Evolution of the Density Contrast with Particle Production in a Gauge-Invariant Formalism

In this work we derive the evolution equation for the density contrast considering open system cosmology, where the influence of adiabatic particle production process on the dynamic of a homogeneous and isotropic is investigated within a manifestly covariant formulation. As application we derive the solution for two sources, one of them is a generalization of Prigogine's model. Then we establish the condition for the reach of the non-linear regime for the density contrast which turns out to be a necessary condition for the structure formation.