Hubble flows and gravitational potentials in observable Universe

Abstract

Abstract. In this paper, we consider the Universe deep inside of the cell of uniformity.At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies), which disturb the background Friedmann model. We propose mathematical models with conformally flat, hyperbolic and spherical spaces. For these models, we obtain the gravitational potential for an arbitrary number of randomly distributed inhomogeneities. In the cases of flat and hyperbolic spaces, the potential is finite at any point, including spatial infinity, and valid for an arbitrary number of gravitating sources. For both of these models, we investigate the motion of test masses (e.g., dwarf galaxies) in the vicinity of one of the inhomogeneities. We show that there is a distance from the inhomogeneity, at which the cosmological expansion prevails over the gravitational attraction and where test masses form the Hubble flow. For our group of galaxies, it happens at a few Mpc and the radius of the zero-acceleration sphere is of the order of 1 Mpc, which is very close to observations. Outside of this sphere, the dragging effect of the gravitational attraction goes very fast to zero.

First-Order Cosmological Perturbations Engendered by Point-Like Masses

“…can be easily determined with the help of the well-known general expression for the matter energymomentum tensor contravariant components (Landau & Lifshitz 2000;Chisari & Zaldarriaga 2011;Eingorn & Zhuk 2012:…”

“…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.…”

“…where K = +1 for the spherical (closed) space and K = −1 for the hyperbolic (open) space, and the Laplace operator is redefined appropriately (see Eingorn & Zhuk (2012); Burgazli et al (2015)). This equation is equivalent to the equation (2.25) in (Burgazli et al 2015) up to designations.…”

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

“…And it is also clear that this system of equations is reduced to (2.18)-(2.20) in [5] for F (R) = 1.…”

“…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].…”