Reexamination of the hierarchy problem from a novel geometric perspective

TL;DR

This paper proposes a novel geometric approach to the hierarchy problem by integrating cosmological models, conformal symmetry breaking, and the de Sitter space radius, linking fundamental constants to cosmological parameters.

Contribution

It introduces a new cosmological model incorporating dark energy, matter, and conformal symmetry breaking, connecting the hierarchy problem to the de Sitter space radius.

Findings

Derived a relation between gravitational coupling and de Sitter radius.

Linked the hierarchy problem solution to the dependence of $R_{dS}$ on cosmological time.

Showed the electromagnetic energy-momentum tensor aligns with Einstein tensor in the model.

Abstract

A lucid interpretation of the longstanding hierarchy problem is proposed based on the unconventional model of the universe recently proposed by the authors. Our heuristic cosmological model is developed by considering Penrose and Petit's original ideas as the Weyl curvature hypothesis, conformal cyclic cosmology, and the twin universe model. The uniqueness of our model lies in its incorporation of dark energy and matter, and its single key parameter, adjusted by observational data, is the radius ($R_{dS}$) of a four-dimensional ($4D$) hypersphere called de Sitter space. We presuppose that our $4D$ universe originated from the spontaneous conformal symmetry (SCS) breaking of a light field with a null distance. We show that in this SCS breaking state, the energy--momentum tensor of the space-like electromagnetic field, whose existence is inevitable for quantum electromagnetic field interactions (Greenberg--Robinson theorem), becomes isomorphic to the divergence-free Einstein tensor in the general theory of relativity. Furthermore, we reveal the $R_{dS}$ dependency of the $4D$ gravitational field. Based on these findings, we show an intriguing relation between the magnitude of the gravitational coupling constant and $R_{dS}$. A solution to the hierarchy problem is derived by assuming that $R_{dS}$ depends on the "newly defined cosmological time".