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We argue that the Standard Model (SM) in the Higgs phase does not suffer from a "hierarchy problem" and that similarly the "cosmological constant problem" resolves itself if we understand the SM as a low energy effective theory emerging from a cutoff-medium at the Planck scale. We actually take serious Veltman's "The Infrared–Ultraviolet Connection" addressing the issue of quadratic divergences and the related huge radiative correction predicted by the SM in the relationship between the bare and the renormalized theory, usually called "the hierarchy problem" and claimed that this has to be cured. We discuss these issues under the condition of a stable Higgs vacuum, which allows extending the SM up to the Planck cutoff. The bare Higgs boson mass then changes sign below the Planck scale, such that the SM in the early universe is in the symmetric phase. The cutoff enhanced Higgs mass term as well as the quartically enhanced cosmological constant term provide a large positive dark energy that triggers the inflation of the early universe. Reheating follows via the decays of the four unstable heavy Higgs particles, predominantly into top–antitop pairs, which at this stage are massless. Preheating is suppressed in SM inflation since in the symmetric phase bosonic decay channels are absent at tree level. The coefficients of the shift between bare and renormalized Higgs mass as well as of the shift between bare and renormalized vacuum energy density exhibit close-by zeros at about 7.7 × 10 14 GeV and 3.1 × 10 15 GeV , respectively. The zero of the Higgs mass counter term triggers the electroweak phase transition, from the low energy Higgs phase and to the symmetric phase above the transition point. Since inflation tunes the total energy density to take the critical value of a flat universe and all contributing components are positive, it is obvious that the cosmological constant today is naturally a substantial fraction of the total critical density. Thus taking cutoff enhanced corrections seriously the Higgs system provides besides the masses of particles in the Higgs phase also dark energy, inflation and reheating in the early universe. The main unsolved problem in our context remains the origin of dark matter. Higgs inflation is possible and likely even unavoidable provided new physics does not disturb the known relevant SM properties substantially. The scenario highly favors to understand the SM and its main properties as a natural structure emerging at long distance. This in particular concerns the SM symmetry patterns and their consequences. [ABSTRACT FROM AUTHOR]

We investigate static and spherically symmetric black hole solutions in the generalized Proca theory which corresponds to the generalization of the shift-symmetric scalar-tensor Horndeski theory to the vector-tensor theory. Any solution obtained in this paper possesses a constant spacetime norm of the vector field, $$X:=-\frac{1}{2}g^{\mu \nu }A_\mu A_\nu =X_0=\mathrm{constant}$$ . The solutions in the theory with generalized quartic coupling $$G_4(X)$$ generalize the stealth Schwarzschild and the Schwarzschild- (anti-) de Sitter solutions obtained in the theory with the nonminimal coupling to the Einstein tensor $$G^{\mu \nu } A_\mu A_\nu $$ . While in the vector-tensor theory with the coupling $$G^{\mu \nu }A_\mu A_\nu $$ the electric charge does not explicitly affect the spacetime geometry, in more general cases with nonzero $$G_{4XX}(X_0)\ne 0$$ this property does not hold in general. The solutions in the theory with generalized cubic coupling $$G_3(X)$$ are given by the Schwarzschild- (anti-) de Sitter spacetime, where the dependence on $$G_3(X)$$ does not appear in the metric function. [ABSTRACT FROM AUTHOR]

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