Primordial Black Holes from Supersymmetry in the Early Universe

Supersymmetric extensions of the standard model generically predict that in the early Universe a scalar condensate can form and fragment into $Q$ balls before decaying. If the $Q$ balls dominate the energy density for some period of time, the relatively large fluctuations in their number density can lead to formation of primordial black holes (PBH). Other scalar fields, unrelated to supersymmetry, can play a similar role. For a general charged scalar field, this robust mechanism can generate black holes over the entire mass range allowed by observational constraints, with a sufficient abundance to account for all dark matter in some parameter ranges. In the case of supersymmetry the mass range is limited from above by $10^{23}\mathrm{g}$. We also comment on the role that topological defects can play for PBH formation in a similar fashion.

Figure 1

Cosmological timeline corresponding to the production of PBH. The orange dashed line denotes radiation density ${\rho }_R$, the blue dashed line is $Q$-ball energy density $⟨{\rho }_Q⟩$, and the black solid line is black hole density $⟨{\rho }_{\mathrm{BH}}⟩$. The inset in the upper right is a zoomed-in view of the early matter dominated era ($t_Q<t<t_R$), with density scaled by $a^3$ (so that nondecaying matter is represented by a straight horizontal line). The horizontal dashed line indicates the observed present-day dark matter density. Here the parameters correspond to the solid line in Fig. 3.

Figure 2

Differential fraction of $Q$-ball energy density transferred to BH density as a function of $\eta =M/M_f$. This spectrum corresponds to the parameters for the solid black line in Fig. 3, which accounts for 100% of the dark matter.

Figure 3

Comparison of the observational constraints on $f\equiv {\mathrm{\Omega }}_{\mathrm{PBH}}/{\mathrm{\Omega }}_{\mathrm{DM}}$ (orange, shaded), with the expected value of ${\tilde{f}}_{\mathrm{BH}}(M)\equiv {\rho }_{\mathrm{DM}}^{-1}d⟨{\rho }_{\mathrm{BH}}⟩/d(\ln M)$ for some hand-picked parameters (black). Parameters for the three curves are $t_f=1.12\times {10}^{-17}\mathrm{s}$, $r_f=1.1$, $r=4.47\times 10^2$, $N_f=10^6$, $f=1$ (solid line), $t_f=2.0\times {10}^{-11}\mathrm{s}$, $r_f=1.1$, $r=1.58\times 10^3$, $N_f=10^6$, $f=0.2$ (dashed line), and $t_f=1.0\times {10}^{-3}\mathrm{s}$, $r_f=1.1$, $r=4.47\times 10^2$, $N_f=10^5$, $f=0.001$ (dot-dashed line).