A simple solution to the monopole problem: SU(5) GUT with symmetry breaking into special subgroup

Abstract

Grand unified theories (GUTs) predict the overproduction of magnetic monopoles, leading to the so-called monopole problem, which is often addressed by cosmological inflation that dilutes their abundance. However, if inflation occurs before the GUT symmetry breaking, monopoles are produced afterwards and the problem persists. This motivates the exploration of alternative mechanisms. We propose a simple solution based on the Langacker--Pi mechanism within an $SU(5)$ GUT framework with symmetry breaking into its special subgroup. In particular, after the gauge symmetry is broken to the Standard Model (SM) gauge group $SU(3)_C\times SU(2)_L\times U(1)_Y$ by the vacuum expectation value of an adjoint scalar, it is further broken to $SO(3)_C\times SO(2)_L$. This structure is naturally realized by introducing a symmetric tensor scalar, a singlet scalar, and multiple singlet fermions. During this intermediate phase, the monopoles become connected to antimonopoles by cosmic strings, which enhances their pair annihilation and reduces their abundance. Subsequently, the symmetry is restored to the SM gauge group. The restoration transition can be either first-order or second-order, depending on the model parameters. In the case of a first-order phase transition, a stochastic gravitational-wave (GW) signal is generated. For a certain region of the parameter space, the resulting signal can lie within the sensitivity of future GW experiments.