Reheating Bounds from Thermal GUT Monopole Production

Abstract

Magnetic monopoles are a generic prediction of Grand Unified Theories (GUTs) that are in tension with modern cosmological and observational bounds. In this paper, we calculate the present-day abundance of GUT monopoles produced thermally in the early Universe. We improve on previous calculations by accounting for full relativistic corrections to the thermal abundance and enhanced monopole annihilation due to the emission of radiation and scattering off massive gauge bosons, the Standard Model fermions and their superpartners. To obtain a present-day energy density less than that of dark matter, we show that the reheating temperature of the Universe, $T_{\rm RH}$, must be less than $0.55$ times the GUT symmetry breaking scale $T_{\rm GUT}$ for the canonical 't Hooft-Polyakov monopole mass. Accounting for Parker bounds on the present-day magnetic monopole abundance, the bound is tightened to $T_{\text{RH}}/T_{\text{GUT}} \lesssim 0.45$. Furthermore, experimental bounds from Super-Kamiokande require $T_{\text{RH}}/T_{\text{GUT}} \lesssim 0.35$ in our scenario.