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

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.