Topological structure of the vacuum, cosmological constant and dark energy

Abstract

In this review we present a theory of cosmological constant and Dark Energy (DE), based on the topological structure of the vacuum. The Multiple Point Principle (MPP) is reviewed. It demonstrates the existence of the two vacua into the SM. The Froggatt-Nielsen's prediction of the top-quark and Higgs masses is given in the assumption that there exist two degenerate vacua in the SM. This prediction was improved by the next order calculations. We also considered B.G. Sidharth's theory of cosmological constant based on the non-commutative geometry of the Planck scale space-time, what gives an extremely small DE density providing the accelerating expansion of the Universe. Theory of two degenerate vacua -the Planck scale phase and Electroweak (EW) phase -also is reviewed, topological defects in these vacua are investigated, also the Compton wavelength phase suggested by B.G. Sidharth was discussed. A general theory of the phase transition and the problem of the vacuum stability in the SM is reviewed. Assuming that the recently discovered at the LHC new resonance with mass m S 750 GeV is a new scalar S bound state 6t + 6t, earlier predicted by C.D. Froggatt, H.B. Nielsen and L.V. Laperashvili, we try to provide the vacuum stability in the SM and exact accuracy of the MPP.

Exotic Lifshitz transitions in topological materials

“…of the first order phase transition, where different vacua have the same energy. [11][12][13][14][15]…”

Explaining Defects of the Universal Vacua with Black Holes-Hedgehogs and Strings

“…As it was shown in Ref. [62], the Planck scale vacuum energy density (with the VEV v 2 ) is equal to: In the above equations "NC" means the "non-commutativity" and "ZPF" means "zero point fields".…”

“…This third vacuum is a very speculative possible state inside the pure SM, which contains a lot of strongly bound states, each bound from 6 top + 6 anti-top quarks (see Refs. [37][38][39][40][41]).…”

“…157non-differentiable space-time: by a foam of black-holes, having lattice-like structure, in which sites are 158 black-holes with "hedgehog" monopoles inside them. This manifold is described by a non-commutative 159 geometry[3,4,[62][63][64][65][66][67][68][69][70][71].160In Refs [3,4]. B.G.…”