Particle number density fluctuations and pressure effects on structure formation

We provide a covariant and gauge-invariant approach to the question of how a first-order pressure can be incorporated self-consistently in a cosmologi cal scenario. The approximation is relevant, in the linear regime, to weakl y self-interacting or warm dark matter models. We also derive number densit y fluctuations in which new modes appear because the number density fluctua tions are no longer simply proportional to the density fluctuations.