Millicharged Scalar Fields, Massive Photons and the Breaking of $SU(3)_{C} \times U(1)_{\rm EM}$

TL;DR

This paper explores the cosmological implications of millicharged scalar fields and massive photons, analyzing symmetry breaking scenarios, constraints on particle charges and masses, and the potential fate of fundamental gauge symmetries in the universe.

Contribution

It provides new limits on millicharged scalars and examines the possible breaking of electromagnetic and strong interactions in cosmological contexts.

Findings

Scalar fields with charge q ≲ 10^{-3}e are viable; heavier scalars are constrained.

Photon mass limit of 10^{-18} eV implies scalar mass of ~10^{-13} eV with charge 10^{-6}e.

Multiple symmetry breaking paths for SU(3)_C are possible, affecting the universe's vacuum stability.

Abstract

Under the assumption that the current epoch of the Universe is not special, i.e. is not the final state of a long history of processes in particle physics, the cosmological fate of $SU(3)_C \times U(1)_{\rm EM}$ is investigated. Spontaneous symmetry breaking of $U(1)_{\rm EM}$ at the temperature of the Universe today is carried out. The charged scalar field $\phi_{\rm EM}$ which breaks the symmetry is found to be ruled out for the charge of the electron, $q=e$. Scalar fields with millicharges are viable and limits on their masses and charges are found to be $q\lesssim10^{-3}e$ and $m_{\phi_{\rm EM}}\lesssim10^{-5} \rm eV$. Furthermore, it is possible that $U(1)_{\rm EM}$ has already been broken at temperatures higher than $T=2.7K$ given the nonzero limits on the mass of the photon. A photon mass of $m_{\gamma}=10^{-18} \rm eV$, the current upper limit, is found to require a spontaneously symmetry breaking scalar mass of $m_{\phi_{\rm EM}}\sim 10^{-13} \rm eV$ with charge $q=10^{-6}e$, well within the allowed parameter space of the model. Finally, the cosmological fate of the strong interaction is studied. $SU(3)_C$ is tested for complementarity in which the confinement phase of QCD $+$ colored scalars is equivalent to a spontaneously broken $SU(3)$ gauge theory. If complementarity is not applicable, $SU(3)_C$ has multiple symmetry breaking paths with various final symmetry structures. The stability of the colored vacuum at finite temperature in this scenario is nonperturbative and a definitive statement on the fate of $SU(3)_C$ is left open. Cosmological implications for the metastability of the vacua - electromagnetic, color and electroweak - are discussed.