The quantum Higgs field and the resolution of the cosmological constant paradox in the Weyl-geometrical Universe

Abstract

The nature of the scalar field responsible for the cosmological inflation is found to be rooted in the most fundamental concept of the Weyl’s differential geometry: the parallel displacement of vectors in curved spacetime. Within this novel geometrical scenario, the standard electroweak theory of leptons based on the [Formula: see text] as well as on the conformal groups of spacetime Weyl’s transformations is analyzed within the framework of a general-relativistic, conformally-covariant scalar–tensor theory that includes the electromagnetic and the Yang–Mills fields. A Higgs mechanism within a spontaneous symmetry breaking process is identified and this offers formal connections between some relevant properties of the elementary particles and the dark energy content of the Universe. An “effective cosmological potential”: [Formula: see text] is expressed in terms of the dark energy potential: [Formula: see text] via the “mass reduction parameter”: [Formula: see text], a general property of the Universe. The mass of the Higgs boson, which is considered a “free parameter” by the standard electroweak theory, by our theory is found to be proportional to the mass [Formula: see text] which contributes to the measured Cosmological Constant, i.e. the measured content of vacuum-energy in the Universe. The nonintegrable application of the Weyl’s geometry leads to a Proca equation accounting for the dynamics of a [Formula: see text]-particle, a vector-meson proposed as an optimum candidate for Dark Matter. The peculiar mathematical structure of [Formula: see text] offers a clue towards a very general resolution in 4-D of a most intriguing puzzle of modern quantum field theory, the “cosmological constant paradox”(here referred to as: “[Formula: see text]-paradox”). Indeed, our “universal” theory offers a resolution of the “[Formula: see text]-paradox” for all exponential inflationary potentials: [Formula: see text], and for all linear superpositions of these potentials, where [Formula: see text] belongs to the mathematical set of the “real numbers”. An explicit solution of the [Formula: see text]-Paradox is reported for [Formula: see text]. The results of the theory are analyzed in the framework of the recent experimental data of the PLANCK Mission. The average vacuum-energy density in the Universe is found: [Formula: see text], the mass-reduction parameter: [Formula: see text] and the value of the “cosmological constant”: [Formula: see text](eV/c[Formula: see text]. A quite remarkable result of the theory consists of the complete formulation of the Einstein equation including in its structure the “cosmological constant”, [Formula: see text]. This was the term that Einstein added “by hand” to his famous equation. The critical stability of the Universe is also discussed.