Scalar and vector perturbations in a universe with discrete and
  continuous matter sources
  We study a universe filled with dust-like matter in the form of discrete
inhomogeneities (e.g., galaxies and their groups and clusters) and two sets of
perfect fluids with linear and nonlinear equations of state, respectively. The
background spacetime geometry is defined by the FLRW metric. In the weak
gravitational field limit, we develop the first-order scalar and vector
cosmological perturbation theory. Our approach works at all cosmological scales
(i.e. sub-horizon and super-horizon ones) and incorporates linear and nonlinear
effects with respect to energy density fluctuations. We demonstrate that the
scalar perturbation (i.e. the gravitational potential) as well as the vector
perturbation can be split into individual contributions from each matter
source. Each of these contributions satisfies its own equation. The
velocity-independent parts of the individual gravitational potentials are
characterized by a finite time-dependent Yukawa interaction range being the
same for each individual contribution. We also obtain the exact form of the
gravitational potential and vector perturbation related to the discrete matter
sources. The self-consistency of our approach is thoroughly checked. The
derived equations can form the theoretical basis for numerical simulations for
a wide class of cosmological models.
