First-order Cosmological Perturbations Engendered by Point-like Masses
  In the framework of the concordance cosmological model the first-order scalar
and vector perturbations of the homogeneous background are derived in the weak
gravitational field limit without any supplementary approximations. The sources
of these perturbations (inhomogeneities) are presented in the discrete form of
a system of separate point-like gravitating masses. The found expressions for
the metric corrections are valid at all (sub-horizon and super-horizon) scales
and converge at all points except at locations of the sources. The average
values of these metric corrections are zero (thus, first-order backreaction
effects are absent). Both the Minkowski background limit and the Newtonian
cosmological approximation are reached under certain well-defined conditions.
An important feature of the velocity-independent part of the scalar
perturbation is revealed: up to an additive constant this part represents a sum
of Yukawa potentials produced by inhomogeneities with the same finite
time-dependent Yukawa interaction range. The suggested connection between this
range and the homogeneity scale is briefly discussed along with other possible
physical implications.
