Accidentally Asymmetric Dark Matter

We study the effect of a first-order phase transition in a confining $SU(N)$ dark sector with heavy dark quarks. The baryons of this sector are the dark matter candidates. During the confinement phase transition the heavy quarks are trapped inside isolated, contracting pockets of the deconfined phase, giving rise to a second stage of annihilation that dramatically suppresses the dark quark abundance. The surviving abundance is determined by the local accidental asymmetry in each pocket. The correct dark matter abundance is obtained for $\mathcal{O}(1–100)\mathrm{PeV}$ dark quarks, above the usual unitarity bound.

Figure 1

Different stages of the phase transition. Top-left panel: Once the universe cools down to slightly below $T_c$, the bubbles of the confined phase (purple regions) start nucleating in a sea of the deconfined phase (light blue regions). Top-middle panel: The nucleated bubbles keep growing until they start running into each other and percolating to make larger bubbles. Top-right panel: Eventually, most of the universe converts to the confined phase, with small, isolated pockets of the deconfined phase. Since isolated quarks (black dots) cannot move into the confined phase, all the quarks, which are, up to this point, well separated, are gathered inside these ever-contracting pockets. Bottom-left panel: a single contracting pocket. The quarks inside it are initially well separated from one another. Bottom-middle panel: As the pocket contracts, the free quarks start annihilating or forming bound states. The color-neutral bound states (orange dots) can move into the confined phase region. Bottom-right panel: Eventually, the pockets disappear. A substantial fraction of quarks annihilate away during the contraction, with the residue surviving in the form of color-neutral baryons that comprise the DM today.

Figure 2

Evolution of the DM abundance. In deriving these plots, the quark pressure effect on the wall velocity is neglected. The figure illustrates that only a fraction of all the initial free quarks in the pocket will end up inside stable baryons and survive the new stage of annihilation at $T=\mathrm{\Lambda }$.

Figure 3

Dark matter parameter space in this setup. The observed DM abundance is obtained for any point on the purple line. The light purple band shows the effect of increasing or decreasing the initial pocket radius by an order of magnitude. Any point above the relic abundance line produces too much dark matter and is ruled out. The DM relic abundance in the entire region is determined by only the accidental asymmetric abundance in each pocket. The contours of constant mass are shown by dashed black lines.