A Casimir bottleneck in primordial large-N baryon formation

Abstract

We study baryon $(\mathcal{B})$ formation in the early Universe in a confining $SU(\mathcal{N})$ gauge theory with quarks transforming in the fundamental representation. Casimir scaling of the confining potential implies that, at large $\mathcal{N}$, $\mathcal{B}$ formation is hindered by a bottleneck: for small quark clusters, representing the initial stages of $\mathcal{B}$ assembly, destruction processes greatly outweigh formation processes. In a $\mathcal{B}$-$\bar{\mathcal{B}}$ symmetric plasma, the relic density of cosmologically stable $\mathcal{B}$'s is set, for large $\mathcal{N}$, during confinement rather than by annihilation freeze-out. This affects relic-density estimates for $SU(\mathcal{N})$ dark matter models.