Remarks on mechanical approach to observable Universe

Abstract

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 10, i.e. approximately for 13 billion years from the present moment. We consider scalar perturbations and, within the ΛCDM 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.

First-Order Cosmological Perturbations Engendered by Point-Like Masses

“…Such a favourable situation is possible owing to the last term in the left-hand side (lhs) of Eq. (2.15), which has been disregarded in (Eingorn & Zhuk 2012) by mistake and erroneously compensated in (Eingorn & Zhuk 2014) by inhomogeneous radiation of unknown nature. Actually, such radiation must not only possess negligible average energy density (requiring additional questionable reasoning), but also exchange the momentum with the nonrelativistic pressureless matter, despite the fact that no non-gravitational interaction between these two constituents has been assumed, and therefore the energy-momentum interchange is strictly forbidden.…”

“…Zero average values of the first-order cosmological perturbations are expected from the very beginning, since these metric corrections are none other than linear deviations from the unperturbed average values of the metric coefficients. Nevertheless, as shown by Eingorn & Zhuk (2014); , there exists a concrete example of the mass distribution, which gives the nonzero average value of the gravitational potential determined by the standard prescription (3.11). This problem is solved by through introducing manually the abrupt cutoff of the gravitational interaction range with the help of the Heaviside step function.…”

Scalar perturbations in cosmological models with quark nuggets

“…At scales much larger than the characteristic distance between these inhomogeneities, the Universe is well described by the homogeneous and isotropic FRW metrics. This is approximately 190 Mpc and larger [23]. At these scales, the matter fields (e.g., cold dark matter) are well described by the hydrodynamical approach.…”

Scalar perturbations in f(R) cosmologies in the late Universe

“…We could describe it by hydrodynamical approach, but inside the cell of uniformity 150 -370 Mpc it is highly inhomogeneous and the hydrodynamical approach is already not adequate. We must use the mechanical approach, [5] and [7].…”