The expansion of the universe was theoretically substantiated by Friedman at the beginning of the 20th century and is the foundation of the modern cosmological theory of the “big bang”. To describe the expanding universe, a corresponding mathematical model has been built based on the Friedmann metric, which assumes three possible states of curvature of the space of our universe — zero curvature for a flat three-dimensional universe, negative for a concave three-dimensional hypersphere of the universe and positive for a curved three-dimensional sphere of the universe. However, this mathematical model is currently only applied on a large scale of the universe. Approximately hundreds of light years or more, which corresponds to the size of galaxy clusters. First of all, such a limitation of the scope of application of the mathematical model of the «expanding universe» is due to the fact that practical measurements of its metrics in the nearest neighborhoods on the scale of galaxies do not confirm its expansion. Of course, theorists have a wonderful rule for such cases, which says that if the observed reality does not correspond to the predictions of the theory, then so much the worse for the observed reality. However, in this case, scientists were able to introduce into their theoretical model, as it were, plausible clarifications, allegedly explaining the absence of expansion of the universe in individual local areas by the fact that on galactic scales, space objects are connected to each other by the force of gravitational attraction and this force keeps such local areas of the universe from expanding…
In the picture above, such stationary, non-expanding regions of the universe are clearly visible as brighter white clusters, forming a kind of cellular structure around black voids — voids. According to modern concepts, the expansion of the universe is not observed inside clusters of galaxies (white regions), since gravity interferes with it (expansion). The expansion of the universe occurs exclusively within the black regions due to the lesser gravitational forces linking the galaxy clusters along the edges of the voids. It sounds quite logical, and at first glance, such a distribution of gravitational fields looks quite plausible. However, in order to assess the legitimacy of the proposed limitation of the scope of the Friedman model, let’s define the magnitudes of the gravitational forces acting on the presented space objects. According to Newton’s formula, the force of gravitational attraction of two material objects is proportional to the masses of interacting objects and is inversely proportional to the square of the distance between them. It is by this formula that theorists build their theories. Let’s apply this formula to test their theories. The mass of an average galaxy is something like 10 ^ 10 (ten to the tenth power) of the mass of the Sun. The average diameter of the galaxy is approximately 400,000 light years. The average distance between galaxies in the cluster is at least 3 million light years. With this data, we can calculate the force of gravitational attraction between average galaxies within an abstract cluster of galaxies.
This very rough calculation gave us the first figure to compare. Let’s carry out similar calculations for the force of gravitational attraction between galaxy clusters located at the maximum distance from each other around black voids. To do this, we need the mass value of the average galactic cluster, as well as the average diameter of the black void (void). So, the average galaxy cluster consists of about 500 galaxies and has a mass of 10 ^ 15 (ten to the fifteenth power) of the solar masses. The diameter of the average galaxy cluster is 19.6 million light years. The average void is roughly 300 million light years across. We consider:
The resulting value is 6 (six) orders of magnitude greater than the force of attraction between individual galaxies within clusters. Those. the force of gravitational attraction between clusters of galaxies separated by voids is a million times greater than the force of attraction of galaxies to each other within a galaxy cluster. Consequently, a mathematical model based on the Friedmann metric will work on the scale of galaxy clusters a million times worse than on the scale of galaxies. Considering that at the present time it does not work at all on the scale of galaxies, we can conclude that this mathematical model is inoperable on any scale of the universe. Thus, by means of simple calculations, the theoretical foundations of the «expansion of the universe» are crossed out.