Gauge-invariant perturbations in a universe with a collisionless gas and a fluid

Bardeen's formalism for cosmological perturbations is extended to a system of a fluid and a collisionless gas which is the best candidate for the dark matter. For the latter kinetic approach is taken and the linearized coupled Einstein-Boltzmann equations are derived. When we solve them, any truncation is not performed in our formalism. Because of gauge-invariance, it is suited especially to the study of perturbations of the dark matter in an early stage of the universe, which grow to eventually form the large scale structure of the universe. (author)