Black-holes-hedgehogs in the false vacuum and a new physics beyond the Standard Model

In the present talk, we consider the existence of the two degenerate universal vacua: a) the first Electroweak vacuum at v = 246 GeV - “true vacuum”, and b) the second Planck scale “false vacuum” at v2 ∼ 1018 GeV. In these vacua, we investigated the different topological defects. The main aim of this paper is an investigation of the hedgehog’s configurations as defects of the false vacuum. In the framework of the f(R) gravity, suggested by authors in their Gravi-Weak Unification model, we obtained a black hole solution, which corresponds to a “hedgehog” - global monopole, “swallowed” by a black-hole with mass ∼ 1019 GeV. These black-holes form a lattice-like structure of the vacuum at the Planck scale. Considering the results of the hedgehog lattice theory in the framework of the SU(2) Yang-Mills gauge-invariant theory with hedgehogs in the Wilson loops, we have used the critical value of temperature for the hedgehog’s confinement phase. This result gave us the possibility to conclude that there exist triplet Higgs fields which can contribute to the SM at the energy scale ≃ 104 ∼ 105 GeV. Showing a new physics at the scale 10÷100 TeV, these triplet Higgs particles can provide the stability of the EW-vacuum of the SM.


The investigation
The talk is devoted to studying of topological defects of the universal vacua and to existence of two degenerate vacua in our Universe.The main ideas are published in Refs.[1,2].
During the expansion after the Planck era, the early Universe underwent a series of phase transitions as a result of which there were arisen such vacuum topological defects (widely discussed in literature) as monopoles or hedgehogs (point defects), strings (line defects), bubbles and domain walls (sheet defects).These topological defects appeared due to the breakdown of local or global gauge symmetries.
This work is essentially based on the discovery that a cosmological constant of our Universe is extremely small, almost zero [3,4,5].We considered a Multiple Point Principle (MPP) first suggested by D.L. Bennett and H.B. Nielsen [6], which predicts the existence in Nature of several degenerate vacua with very small energy density (cosmological constants).The model developed in this article confirms the existence of the two degenerate vacua of the Universe: The first ("true") Electroweak (EW) vacuum with VEV v 1 ≈ 246 GeV, and the second ("false") Planck scale vacuum with VEV v 2 ∼ 10 18 GeV.
The main idea of this investigation is the hedgehog's configurations [7,8] as defects of the false vacuum.We have shown that at superhigh (Planck scale) energies the black-holes-hedgehogs are responsible for the creation of the false vacuum of Universe.In the framework of the f (R) gravity, we have obtained a solution for a global monopole, which is a black-hole-hedgehog at the Planck scale.Here we have used the f (R) gravity predicted by the Gravi-Weak unification model previously developed by authors in papers [9,10,11,12,13].
Using the results of Refs.[14,15] obtained for the SU (2) Yang-Mills theory of the gaugeinvariant hedgehog-like structures in the Wilson loops, we have considered the lattice theory giving the critical value of temperature for the hedgehogs confinement phase.Considering the hedgehog lattice theory, we have concluded that hedgehogs can exist only at the energy scale µ 10 4 GeV.Triplet Higgs fields Φ a (with a = 1, 2, 3), which are responsible for the formation of hedgehogs, can show a new physics at the scale ∼ 10 TeV.
We reviewed the Multiple Point Principle (MPP) suggested by D.L. Bennett and H.B. Nielsen [6].In the assumption of the existence of the two degenerate vacua (Electroweak vacuum at v 1 ≈ 246 GeV, and Planck scale one at v 2 ∼ 10 18 GeV), Froggatt and Nielsen [16] obtained the first prediction of the top-quark and Higgs boson masses, which was further improved by several authors in the next approximations.We devoted to the general properties of topological defects of the universal vacua.We considered topological defects in the "false vacuum", which is presented as a spherical bubble spontaneously produced in the de Sitterlike universe.The space-time inside the bubble, which we refer to as a "true vacuum", has the geometry of an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe.The Gravi-Weak unification (GWU) model [9,10,11,12,13] as an example of the f (R) gravity.We considered the existence of the de Sitter solutions in the Planck phase.In our calculations of parameters of the GWU-model, where we predicted the Planck scale false vacuum VEV equal to v 2 ≈ 6.28 × 10 18 GeV.We have investigated the hedgehog's configurations as defects of the false vacuum and we obtained a solution for a black-hole in the framework of the f (R) gravity, which corresponds to a global monopole "swallowed" by a black-hole.The metric around of the global monopole was considered.The mass M BH , radius δ and "horizon radius" r h of the black-hole-hedgehog were estimated.The lattice-like structure of the false vacuum which is described by a non-differentiable space-time: by a foam of black-holes, having latticelike structure, in which sites are black-holes with "hedgehog" monopoles inside them.This manifold is described by a non-commutative geometry predicted an almost zero cosmological constant.The phase transition from the "false vacuum" to the "true vacuum", where it was shown that the Electroweak spontaneous breakdown of symmetry SU (2) L ×U (1) Y → U (1) el.mag created new topological defects of EW vacuum: the Abrikosov-Nielsen-Olesen closed magnetic vortices ("ANO strings") of the Abelian Higgs model and Sidharth's Compton phase objects.Then the "true vacuum" (EW-vacuum) again presents the non-differentiable manifold with noncommutative geometry, and again has an almost zero cosmological constant.Here we estimated the black-hole-hedgehog's mass and radius: M BH ≈ 3.65 × 10 18 GeV and δ ≈ 0.29λ P l ≈ 10 −21 GeV −1 near the second vacuum v 2 .We emphasize that due to the energy conservation law, the vacuum density before the phase transition is equal to the vacuum density after the phase transition, and we have ρ vac (at Planck scale) = ρ vac (at EW scale).Therefore, we confirmed the Multiple Point Principle: we have two degenerate vacua v 1 and v 2 with an almost zero vacuum energy (cosmological constants).This means that our EW-vacuum, in which we live, is stable.The Planck scale vacuum cannot be negative: (vii) By solving the gravitational field equations we estimated the black-hole-hedgehog's mass, radius and horizon radius are M h ≈ 3.65 × 10 18 GeV, R h ∼ 10 −21 GeV −1 and r h ≈ 2.29R h respectively.(viii) We considered that due to the energy conservation law, the vacuum energy density before the phase transition is equal to the vacuum energy density after the phase transition: ρ vac (at Planck scale) = ρ vac (at EW scale).This result confirms the Multiple Point Principle: we have two degenerate vacua v 1 and v 2 with an almost zero vacuum energy density (cosmological constants).By these considerations we confirmed the vacuum stability of the EW-vacuum, in which we live.The Planck scale vacuum cannot be negative because of the exact equality V ef f (min 1 ) = V ef f (min 2 ).(ix) Hedgehogs in the Wilson loops of the SU (2) Yang-Mills theory, and phase transitions in this theory were investigated revising the results of Refs.[14,15].Using their lattice result for the critical value of the temperature of hedgehog's confinement phase: β crit ≈ 2.5, we predicted the production of the SU (2)-triplet Higgs bosons at LHC at energy scale µ ∼ 10 TeV, providing a new physics in the SM.(x) We considered an additional confirmation of the vacuum stability and accuracy of the MPP taking into account that hedgehog fields Φ a produce a new physics at the scale ∼ 10 TeV, and calculating at high energies the contribution of the black-hole-hedgehog corrections to the effective Higgs potential.This result essentially depends on the hedgehog field parameters: mass, radius and mixing coupling constant λ hH of the interaction of hedgehogs with the SM doublet Higgs fields H. (xi) Please see ref. [17] for detail investigation.