Interactions from SSB of scale symmetry: applications to problems of quintessence, galaxy dark matter and fermion family

TL;DR

This paper explores a scale-invariant two-measure theory with a dilaton field, revealing a new mechanism for exponential potential generation, and discusses implications for quintessence, dark matter, and fermion families.

Contribution

It introduces a novel approach where spontaneous symmetry breaking yields exponential potentials and multiple fermion types, addressing dark matter and particle family problems.

Findings

Exponential potential arises after scale symmetry breaking.

Three distinct fermion types emerge, suggesting a new approach to fermion families.

Two fermion types have constant masses and no fifth force, while the third interacts differently.

Abstract

We study a scale invariant two measures theory where a dilaton field \phi has no explicit potentials. The scale transformations include a shift \phi\to\phi+const. The theory demonstrates a new mechanism for generation of the exponential potential: in the conformal Einstein frame (CEF), after SSB of scale invariance, the theory develops the exponential potential and, in general, non-linear kinetic term is generated as well. The possibility of quintessence and of halo dark matter solutions are shown. The regime where the fermionic matter dominates (as compared to the dilatonic contribution) is analyzed. There it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles in CEF that appears to suggest a new approach to the family problem of particle physics. It is automatically achieved that for two of them, fermion masses are constants, gravitational equations are canonical and the "fifth force" is absent. For the third type of particles, four fermionic interaction appears from SSB of scale invariance.