Mass Constituents of a Flat Lattice Multiverse: Conclusion from Similarity between Two Universal Numbers, the Rocksalt-Type 2<i>D</i> Madelung Constant and the Golden Mean

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 &phi;=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 &phi; , one reaches again 1 + &phi; as the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3 D lattice a flat 2 D one of rocksalt type, the numerical similarity between the Madelung constant and φ &minus; 1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number &phi; 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 &pi; , 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.