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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.

journal of modern physics

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