The 4-Sphere model for an Alternative Metric in Cosmology
Proposing a different calculation for the Galactic Recession, we intend to show the opportunity to modify the Standard Cosmological Model ΛCDM choosing a new metric, other than FLRW.
Everything is described in 4-SPHERE FEATURE AND SPECULATION,
an essay that explores the opportunity to build an alternative cosmological model: The 4-Sphere Model.
|
License:
Creative Commons Attribution-ShareAlike 4.0 International Public License
4-Sphere does not need the Einstein's Cosmological constant Λ
4-Sphere foresees an isochoric phase in the absence of expansion and, although does not have a Horizon Problem, it has no difficulty to accept Inflation as an initial phase in which the expansion manifests itself exponentially.
However unlike ΛCDM, given the characteristic of this new Metric Tensor, our model never needs the corrective parameter Λ, which Einstein had to introduce later in his Field Equation as Cosmological Constant [*]. In fact, the 4-Sphere Metric Tensor contains the term 'R' which characterizes the Galactic Recession, also able to represent both the Inflation and the Isochoric phases, suitably interpreting the quantity c.
All this is very important because, in our conjecture, we feel entitled to extend the laws of our physics to each Big Bang Era, using the most powerful tool we have so far: Einstein's Relativity in its initial form, widely verified in nature. The only condition is that the phenomenon to be studied must take place on the surface of the hypersphere, and that the gravitational range is small enough.
The previous expression: ds2 = -hrξd(rξ)2+htc2dt2 was a particularly interesting hypothesis due to the same constant c present both in the speed of light and in the expansion rate of the Universe. But if we now want to keep the same expression valid for both Inflation and the Isochoric period, said hypothesis loses some of its strength.
However, still remaining within the realm of pure conjecture, we are not far from the logic of 4-Sphere if we assume that the constant c of the speed of light is directly linked to the Universe expansion only if the latter occurs in equilibrium conditions.
[*] – Λ represents a new mathematical entity that Einstein introduced without any direct observational justification. He was aware that this choice could potentially violate the principle of conservation of energy and momentum, and perhaps even the equivalence principle; he later referred to the introduction of
Λ as "the biggest blunder of my life."
However, the cosmological constant was subsequently reassessed in light of discoveries regarding the accelerating universe model (dark energy) in the 1990s.
The 4-Sphere model was conceived with the intention of separating galactic recession from relativity, but it ultimately also falls within a context where (as confirmed by its application of the Doppler effect to galactic recession) the term
cθ for recession is equivalent to the constant Λ.
However, I believe that this possible weakness of the model can be accepted, as it follows the path taken by modern physics. Moreover, as it has been set up to now, this quantity does not influence light (here, the second principle of Relativity is guaranteed by the assumed geometry) but only matter and does not concern gravitational phenomena because where they are perceived the galactic recession is negligible.
|