Does space ever stop expanding, or trying to, regardless of scale?

v. 3. n. 11

The title question has two parts:

1. expanding space, or kinetic energy, or dark energy (cosmological constant), or proposed fundamentally repulsive gravity.
2. static or compressed space, or potential energy, or dark matter, or proposed apparently attractive gravity.

The question at present involves the second aspect, the part between the commas in the title; the first part was briefly discussed in the previous Letter. Even though space at the level of clusters of galaxies, i.e., the Local Group, and below does not appear to expand, this does not necessarily mean that it will not if isolated from the larger scales and given the chance to possibly expand.

The schematic drawing in the cover image is of the Local Group of 50 galaxies, of about five million light years in radius; these galaxies do not appear to be taking part in the Hubble expansion, and make up a stable gravitational unit, with the individual galaxies moving within and not escaping the inner circle. The outer circle would contain all the galaxies within the Local Supercluster of galaxies where the accelerated Hubble expansion is observed.

Applying the following scale-invariant relation to the Local Group

m/r^2 = A/G

where the observed radius r ≈ 5 x 10^6 light years, and where the acceleration of the Local Supercluster, A ≈ 6 x 10^-13 m/s^2. * It follows that mass, m, of the Local Group to include "dark matter" would be about the conventional estimate. Then the question, how could the acceleration of the Local Supercluster supposedly driven by "dark energy" be party to the calculation of the total mass/energy of the non-accelerating Local Group supposedly contained by "dark matter"?

How could the acceleration of the Local Supercluster be party to the calculation of the total mass/energy of the non-accelerating Local Group?

For perspective, in the above Equation let the radius be that of the known Universe, r = 93/2 billion light years, and let A be the acceleration of the Universe at large. ** The resulting calculated mass of the known Universe would be m ≈ 10^50 kg, about the conventional estimate. Again the question, how can the mass of the known Universe to include visible matter, dark energy, and dark matter, be calculated with the same relation as for the Local Group, supposedly containing only visible matter, dark matter but no dark energy? The relation does not distinguish among visible matter, dark matter and dark energy. Since the relation is derived from unmodified Newtonian gravity applied to expanding space with or without visible matter, then the four supposed distinct items -- gravity, visible matter, dark matter and dark energy -- could be fundamentally indistinguishable, as also discussed in previous Letters, all stemming from gravitation.

To the point and the part of the title question between the commas -- given the Local Group of galaxies and space within radius r of the cover image isolated from the rest of the known Universe -- would the individual galaxies still be contained, or would they disperse? In other words, is the space among all visible matter regardless of scale of the same kind and gravitational in nature that is in different states of stress (curvature), having energy that is potential, conventionally referred to as dark matter (i.e., among the Local Group) or kinetic, conventionally referred to as dark energy (among the Local Supercluster and Universe at large)?

______

* (4) An explanation of dark matter and dark energy from unmodified Newtonian gravity* | LinkedIn

** Importance of a value for acceleration of the Universe | LinkedIn

Cover image caption: Local Cluster of galaxies within r. Local Supercluster within R. Not to scale.

Closing image credit: https://www.google.com/url?sa=i&url=https%3A%2F%2Fwww.freepik.com%2Ffree-photos-vectors%2Fspace-background&psig=AOvVaw2i0KCFW5KtnLnrZzC0h02q&ust=1668620614730000&source=images&cd=vfe&ved=2ahUKEwiIxqip3rD7AhUNrXIEH