Hypersphere cosmological model: Expansion Dark Matter Dark Energy

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Hypersphere's other aspects: Universe expansion does not need for Dark Matter or Dark Energy

Dark Energy has been excluded in 4-Sphere among the forces that govern the equilibrium of the Universe in its shape. More precisely as we can see in the speculation, the conjecture predicts that the Universe in its expansion crosses a continuum of states of equilibrium between gravity and pressure of the CMB.

Given the hypothesized estimate of its presence in the Universe, the importance of Dark Matter is fundamental. Questioning its existence is a must and is done in App. 4 [*].

As for Dark Energy, the model does not need Dark Matter. Moreover we will also show that, once we hypothesize a different velocity for the Galactic Recession, their introduction into our physics is probably no longer necessary.

Furthermore, 4-Sphere bases the physics of its model on Cosmic Background Radiation. The following discussion, fundamental to the whole conjecture, could not be missing. The temperature anisotropies of the CMB are described in App. 5 [*]. There, we will show how the analysis of the CMB temperature dipoles could lead to a further verification of the 4-Sphere geometry.

Another important consideration in two points is:

1. With FLRW, at least theoretically, we could observe the oldest Eras of the Universe. It is this aspect that could lead to the crisis of the Standard Model: if a galaxy were found to be too young for the ΛCDM itself, a big problem could arise.
2. With 4-Sphere and its Timelike zone of Special Relativity, that ends with rays of light from a Universe over 5 billion years old, this problem does not exist. (Except CMB, we cannot see light beams originating from a Universe younger than 5 billion years)

Lastly I would like to report the clarity of its definitions (such as that of Proper Distance and Luminosity Distance) with its extreme simplicity of the use of the associated quantities. The short study in App. 6 [*] highlights the fluency of use of these formulas. The adopted Galactic Coordinate system [**] for the model (not used in the study) is also extremely powerful. Once Celestial Longitude, Colatitude and the new one “Height" have been calculated, these remain fixed over time, changing only the increasing radius of the hypersphere: the entire 4-Sphere star map is fixed, only the star distances are time dependent!

[*] – These topics are all described in 4-SPHERE FEATURE AND SPECULATION.
[**] – See Chapter 3.5 in 4-SPHERE FEATURE AND SPECULATION.