Cosmological consequences of spontaneous symmetry breaking

TL;DR

This work develops and applies the concept of accidents—light elementary scalars arising from spontaneously broken large-representation sectors with accidentally flat directions—to cosmology. Accidents provide natural candidates for dark matter and can act as inflatons in hybrid inflation, with radiative corrections lifting their flat directions and preserving light masses. The framework additionally yields a rich topological-defect sector (monopoles, cosmic strings, domain walls) that sources stochastic gravitational waves, and it explores dark monopole production and annihilation dynamics, showing monopoles cannot dominate DM in the dark SO(3) model. The thesis further analyzes topological defects and their GW signatures, and demonstrates how accident-induced inflation can produce detectable gravitational waves and nontrivial CMB observables, offering a coherent path to connect beyond-Standard-Model particle content with cosmological observations. Overall, accidents open new avenues to address naturalness, dark matter, inflation, and gravitational-wave phenomenology within a unified spontaneous-symmetry-breaking context.

Abstract

The Standard Model of particle physics and the $Λ$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.

Figures (21)

• Figure 2. 1: One-loop contributions to the light scalar two-point function. We include, among the radiative corrections, also the diagram arising from the counterterm.
• Figure 2. 2: Even if the Higgs does not couple directly to NP, gravity will mediate the interaction between the new sector and the SM, via a top quark loop.
• Figure 2. 1: Sum of 1PI, connected diagrams contributing the one-loop effective potential in the theory defined in Eq. \ref{['eq:RealScalar']}.
• Figure 2. 1: Left-hand panel. Sketch of the evolution of the thermal effective potential in Eq. \ref{['eq:VSOPT']} for different values of $T$. At large temperatures, the symmetry-preserving point $\phi=0$ is stabilised by thermal corrections. At $T=T_0$, the origin turns into a maximum of the potential. Right-hand panel. Same as in the left-hand panel, but for the potential in Eq. \ref{['eq:VFOPT']}, giving a FOPT. The main difference with respect to the SOPT scenario presented in the left-hand plot is the presence of a barrier separating two minima. For $T<T_c$, the minimum at the origin becomes metastable and the PT occurs via bubble nucleation.
• Figure 3. 1: Left-hand panel. Comoving number density of a thermal population of $\chi$ for different values of the annihilation cross-section, obtained by numerically solving Eq. \ref{['eq:BoltzmannChiApprox']} (solid lines). For $z\sim 1$, $\chi$ becomes non-relativistic and its number density gets exponentially suppressed. Around $z\sim 20 - 30$ the process keeping $\chi$ in thermal equilibrium freezes-out: the comoving number density stops tracking the equilibrium one (black dashed line), and quickly approaches the analytic estimate given in Eq. \ref{['eq:YChiFO']} (colored dashed lines). The green lines give $h^2 \Omega_\chi \simeq 0.12$ today. Right-hand panel. Comoving number density of $\chi$ frozen in by the process $1 \rightarrow \chi\,2$, for $m_1 = 1\,{\rm TeV}$. The solid lines represent the numerical solution to Eq. \ref{['eq:YChiFI']}, while the dashed ones show the asymptotic value for $z\rightarrow \infty$, given in Eq. \ref{['eq:YChiFI0']}. Along the green lines the relic abundance of $\chi$ matches the measured one for $m_\chi = 1\,{\rm MeV}$.