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 Sidharth’s theory of cosmological constant based on the noncommutative 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 — is also reviewed, topological defects in these vacua are investigated, also the Compton wavelength phase suggested by Sidharth is discussed. A general theory of the phase transition and the problem of the vacuum stability in the SM is reviewed. Assuming the existence of a new scalar [Formula: see text] bound state [Formula: see text], earlier predicted by Froggatt, Nielsen and Laperashvili, we try to provide the vacuum stability in the SM and exact accuracy of the MPP.