# The Higgs field and the resolution of the Cosmological Constant Paradox in the Weyl geometrical Universe

## TL;DR

This paper proposes a conformally covariant scalar tensor theory within Weyl geometry to address the cosmological constant paradox, linking Higgs mechanisms, dark energy, and dark matter dynamics, consistent with recent experimental data.

## Contribution

It introduces a novel Weyl geometric framework connecting Higgs physics, dark energy, and dark matter, providing a potential resolution to the cosmological constant paradox.

## Key findings

- Lambda equals six times the effective potential magnitude
- The paradox arises from an algebraic mismatch of scalar field functions
- The theory aligns with recent PLANCK data and supports exponential inflationary models

## Abstract

The standard electroweak theory of leptons and the conformal groups of spacetime Weyl's transformations are at the core of a general relativistic, conformally covariant scalar tensor theory aimed at the resolution of the most intriguing enigma of modern Physics: the cosmological constant paradox (hereafter: Lambda paradox. A Higgs mechanism within a spontaneous symmetry breaking process offers formal connections, via an effective potential V(eff), between some relevant properties of the elementary particles and the dark energy content of the Universe. The nonintegrable application of the Weyl's geometry leads to a Proca equation accounting for the dynamics of a vector-meson proposed as an optimum candidate for Dark Matter. The average vacuum-energy density in the Universe and the "cosmological constant" are evaluated on the basis of the recent experimental data of the PLANCK Mission. The resolution of the paradox is found for all exponential inflationary potentials and is consistent with the experimental data. The result of the theory: Lambda=6|V(eff)|shows that the paradox is determined by the algebraic mismatch between two large counteracting functions of the scalar field contributing to V(eff). The critical stability of the Universe is discussed.