Cosmic Coincidences of Primordial-Black-Hole Dark Matter

If primordial black holes (PBHs) contribute more than 10% of the dark matter (DM) density, their energy density today is of the same order as that of the baryons. Such a cosmic coincidence might hint at a mutual origin for the formation scenario of PBHs and the baryon asymmetry of the Universe. Baryogenesis can be triggered by a sharp transition of the rolling rate of inflaton from slow-roll to (nearly) ultraslow-roll phases that produce large curvature perturbations for PBH formation in single-field inflationary models. We show that the baryogenesis requirement drives the PBH contribution to DM, along with the inferred PBH mass range, the resulting stochastic gravitational wave background frequency window, and the associated cosmic microwave background tensor-to-scalar ratio amplitude, into potentially observable regimes.

Figure 1

The final baryon asymmetry in radiation domination with $\delta =-3.15$, $m_{\sigma }=H_{*}/2$, $\mathrm{\Lambda }=0.3M_P$, where $H_{*}=2.37\times {10}^{13}\mathrm{GeV}$ and ${\mathrm{\Gamma }}_{\varphi }={10}^{13}\mathrm{GeV}$ are used.

Figure 2

(Upper panel) Contours of the final baryon asymmetry $|Y_B|$ in radiation domination with $\delta =-3.15$, $m_{\sigma }=H_{*}/2$, $\mathrm{\Lambda }=0.3M_P$, where $H_{*}=2.37\times {10}^{13}\mathrm{GeV}$ and ${\mathrm{\Gamma }}_{\varphi }={10}^{13}\mathrm{GeV}$ are used. The region $2.506<N_{*}<2.515$ corresponds to the PBH-to-DM ratio $0.1<f_{\mathrm{PBH}}<1$ for $\delta =-3.15$ at the pivot scale $k_0=9.46\times {10}^{13}{\mathrm{Mpc}}^{-1}$. (Lower panel) $f_{\mathrm{PBH}}$ and $|Y_B|$ as functions of $N_{*}$ at $N_{\mathrm{end}}=20$ and $\delta =-3.15$ from $f_{\mathrm{PBH}}=1$ at $N_{*}=2.515$ to $f_{\mathrm{PBH}}={10}^{-50}$ at $N_{*}=2.3$.

Figure 3

The PBH mass function based on the fiducial Press-Schechter statistics at $N_{\mathrm{end}}=20$ with various choices of $\delta$, where $N_{*}$ is fixed by the condition $f_{\mathrm{PBH}}=1$. The pivot scale $k_0=9.46\times {10}^{13}{\mathrm{Mpc}}^{-1}$ is used. Existing observational constraints are also shown, using the publicly available code plotbounds. EGRB is extragalactic gamma-ray background, NS is neutron star, WD is white dwarf.