Cosmological consequences of spontaneous symmetry breaking

Abstract

The Standard Model of particle physics and the $\Lambda$CDM model of cosmology provide an incomplete description of our Universe. Both models face challenges, including explaining the nature of dark matter, the origin of the Universe's initial conditions, and the fine-tuning of the Higgs boson mass. This thesis investigates the cosmological implications of spontaneous symmetry breaking to address some of these issues, focusing on theories with a non-trivial vacuum structure. We introduce a novel class of elementary scalars called ''accidents'', which emerge as accidentally flat directions in the vacuum manifold: unlike Nambu-Goldstone boson directions, accident directions are not related to any symmetry. Radiative corrections induce a mass for the accidents that is one-loop suppressed with respect to naive expectations, making them naturally light. We propose that accidents can act as viable dark matter candidates, and as the inflaton driving cosmic inflation. We construct a model of hybrid inflation in which the inflaton potential is an accident direction and is naturally flat. In models of accident inflation where the vacuum manifold has a non-trivial topology, cosmic strings and domain walls form after the end of inflation. Such topological defects generate a stochastic background of gravitational waves. Finally, we investigate the cosmological production of dark magnetic monopoles. Focusing on 't Hooft-Polyakov monopoles from SO(3)$\rightarrow$SO(2) symmetry breaking, we explore both second-order and first-order phase transitions, and we identify the regions of parameter space where the monopole relic density matches the one of dark matter. This model also features stable massive gauge bosons. We find that the relic density of dark gauge bosons is always far larger than the one of monopoles, concluding that dark monopoles cannot constitute a sizeable fraction of dark matter.