Topological Structure of the Vacuum, Cosmological Constant and Dark Energy

TL;DR

This review explores the topological structure of the vacuum in the Standard Model, discussing multiple vacua, the cosmological constant, dark energy, and their implications for vacuum stability and particle mass predictions.

Contribution

It integrates topological vacuum structure, the Multiple Point Principle, and non-commutative geometry to explain dark energy and predict particle masses, offering a unified theoretical framework.

Findings

Existence of two degenerate vacua in the Standard Model.

Prediction of top-quark and Higgs masses consistent with observations.

Theoretical support for a small cosmological constant from non-commutative geometry.

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 $m_S \simeq 750$ GeV is a new scalar $S$ bound state $6t + 6\bar t$, 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.