Hubble flows and gravitational potentials in observable Universe

TL;DR

This paper models gravitational potentials in the observable universe considering inhomogeneities, showing how local gravitational effects transition to cosmic expansion at certain scales, aligning with observations.

Contribution

It introduces mathematical models for gravitational potentials in inhomogeneous universe regions using conformally flat, hyperbolic, and spherical spaces, with finite potentials at all points.

Findings

Potential is finite at all points in flat and hyperbolic models.

Test masses transition from gravitational attraction to Hubble flow at a few Mpc.

Zero-acceleration sphere radius is about 1 Mpc, matching observations.

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.