Abstract
In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ=0.6180339887, yielding for dark energy to matter mass fractions . Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be , and further the ratio of dark matter to baryonic one . If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield . Replacing the “Madelung” constant α of Villata’s “lattice universe” by φ, one reaches again 1 + φ as the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3D lattice a flat 2D one of rocksalt type, the numerical similarity between the Madelung constant and φ−1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number φ may indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the Archimedes’ constant π, giving for respectively for the dark components . However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.
Highlights
IntroductionSince the discovery of the fivefold symmetry of quasicrystals, the present author as a crystallographer followed the appearance of this symmetry in nature
In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean φ = 0.6180339887, yielding for dark energy to matter mass fractions
Since the discovery of the fivefold symmetry of quasicrystals, the present author as a crystallographer followed the appearance of this symmetry in nature
Summary
Since the discovery of the fivefold symmetry of quasicrystals, the present author as a crystallographer followed the appearance of this symmetry in nature. Familiar with the Fibonacci number sequence and the most irrational universal number of the golden mean, the motivation was obvious to deal with the Penrose universe, too Follow this idea and consider two numerically comparable universal numbers, which may be suitable to combine theoretical approaches that deal with the secrets of our universe. The second number is the Madelung constant α2D = 1.6155426267 of a 2D rocksalt-type lattice, familiar for crystallographers and material scientists that deal with ionic surfaces. It is found in Finch’s monograph about Mathematical Constants [8]. We ask for similarities between El Naschie’s E-infinity theory [5] [6] and Villata’s lattice universe [9], respectively Hajdukovic’s theory of the gravitational polarization of the quantum vacuum [10]
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