Finally, in this section, we will summarize the properties of the universe at the large scale according to Geometric Generalization’s point of view.

In previous chapters, we discussed that the basis of physical reality is a closed elliptic (like spherical) and expanding geometry, which is a result of logical principles that suggests this geometry to be self-coherent (causal) to be real (Section 4.2 and 4.3). Additionally, we explained that Hubble’s expanding space, which we practically observe now, is a universally strained and collapsed state of this logical geometry (Section 5.2).

According to this point of view, we can assume that the universe we observe now should also have the opposite properties of closeness and expansion intrinsically, because our current Hubble’s universe is a (wrinkled) state of our logical geometry.

The property of closeness implies a universe whose spatial directions have finite lengths, but they are unbounded. This can be visualized by closing a one-dimensional geometric object (line) into a circle. Although the size of the circumference should have a finite length, it is possible to move on circumference without encountering any borders or endpoints.

Closeness in spatial dimensions indicates that there should be a curvature in spatial directions. This curvature is positive (like spherical), which means that the surface (space) always lies on the same side of its tangent plane. In other words, all spatial directions are curved towards the same hyper-direction.

On the other hand, according to the property of the expansion, spatial dimensions constantly expand omnidirectionally; therefore, curvature, which is an unnatural state, relaxes and decreases constantly.

Unfortunately, there seems to be no direct clues about the future of our geometry towards time direction, since the ratio of the universal strain on the expansion (Hubble’s constant) might be affected within physical reality. Therefore, it seems that logical reasoning is the only tool to deduce the future of the expansion. We will discuss this subject in Chapter 12 on “Self-Organization, Consciousness, and Future of the Universe”.

According to Geometric Generalization, the mechanism that forms matter and energy in the universe (against the universal strain on the expansion, Section 5.3) suggests homogeneous distribution of matter in the universe. In fact, it can be observed that the average density of matter in large scale is approximately the same in all places in the universe.

Additionally, homogeneity of matter content implies that the strain on the expanding space should be homogenous in all places. It is also observed that Hubble’s constant is also the same in all directions, and it seems to be the same in all places in the universe. Hence, we may assume that the obliquity angle in the wrinkling epoch should be isotropic, and this results in an almost spherical the universe.

Although, it differs to be in motion in spherical space (Section 9.3), the universe looks the same in all directions (in large scales), and there are no preferred directions or special locations in the universe (since space has a positive curvature). Therefore, there are no special points of origin to orient coordinate systems.

Eventually, from the view through time dimension, it can be said that space (as three-dimensional sphere) is orientable (a consistent concept of clockwise rotation can be defined on the surface of our three-dimensional sphere in a continuous manner). This property means that the spin property of a strain package (quantum of matter) will not flip, if that strain package could circulate all around the universe. Additionally, orientability from the view of time dimension causes the conserved property of electric charge. We will detail these properties in next chapter on “Formation Principles of Elementary Particles”.

In previous chapters, we discussed that the total matter - energy content in the universe was not determined at an initial state, and it was not scattered because of a mysteriously embedded energy potential. Instead, matter content in the universe is formed against the universal strain on the expansion (the inflationary epoch to Hubble’s space). Hence, matter content in the universe is a function of the universal strain on the expansion, and matter content in the universe and Hubble’s constant, which indicates the ratio of the universal strain on the expansion, is directly dependent to each other.

Consequently, the variation of the total matter content in the universe (by the means of gravity and electromagnetic radiation) affects the rate of Hubble’s constant, which has extensively happened at the end of the inflationary epoch (Section 7.12).

Additionally, in Section 7.4, we concluded that the strength of electromagnetic interaction (fine structure constant) also indicates the ratio of the universal strain on the expansion (like atmospheric pressure). Indeed, fine structure constant seems to be the most practically observed parameter that indicates the ratio of the universal strain on the expansion (the ratio of the increase in circumference’s (space) size between the inflationary epoch and Hubble’s space).

In Section 9.1, we discussed that physical reality is formed of nothingness (by deviating from nothingness state towards a balanced oppositeness), instead of a coincidental scattering of energy, and we stated that sum of the stress contents in the universe balance each other to make nothingness.

Consequently, the strength of electromagnetic interaction (fine structure constant as a low ratio of compression) indicates that the ratio of the universal strain on the expansion is rather low. Interestingly, although the physical environment in which we humans live are full of matter, low compression ratio suggests that average matter density in the universe should be also low. This conclusion suggests that deviation from the nothingness state is very weak, and contents of the universe are almost nothing, too. Empirically, it seems that there is approximately only one hydrogen atom per 10 cubic meters in the universe.