Remarks on mechanical approach to observable Universe
  We consider the Universe deep inside the cell of uniformity. At these scales,
the Universe is filled with inhomogeneously distributed discrete structures
(galaxies, groups and clusters of galaxies), which perturb the background
Friedmann model. Here, the mechanical approach (Eingorn & Zhuk, 2012) is the
most appropriate to describe the dynamics of the inhomogeneities which is
defined, on the one hand, by gravitational potentials of inhomogeneities and,
on the other hand, by the cosmological expansion of the Universe. In this
paper, we present additional arguments in favor of this approach. First, we
estimate the size of the cell of uniformity. With the help of the standard
methods of statistical physics and for the galaxies of the type of the Milky
Way and Andromeda, we get that it is of the order of 190 Mpc which is rather
close to observations. Then, we show that the nonrelativistic approximation
(with respect to the peculiar velocities) is valid for $z \lesssim 10$, i.e.
approximately for 13 billion years from the present moment. We consider scalar
perturbations and, within the $\Lambda$CDM model, justify the main equations.
Moreover, we demonstrate that radiation can be naturally incorporated into our
scheme. This emphasizes the viability of our approach. This approach gives a
possibility to analyze different cosmological models and compare them with the
observable Universe. For example, we indicate some problematic aspects of the
spatially flat models. Such models require a rather specific distribution of
the inhomogeneities to get a finite potential at any points outside gravitating
masses. We also criticize the application of the Schwarzschild-de Sitter
solution to the description of the motion of test bodies on the cosmological
background.
