Baryogenesis through asymmetric Hawking radiation from primordial black holes as dark matter

We examine the extent to which primordial black holes (PBHs) can constitute the observed dark matter while also giving rise to the measured matter-antimatter asymmetry and account for the observed baryon abundance through asymmetric Hawking radiation generated by a derivative coupling of curvature to the baryon-lepton current. We consider both broad and monochromatic mass spectra for this purpose. For the monochromatic spectrum we find that the correct dark matter and baryon energy densities are recovered for peak masses of the spectrum of $M_{\mathrm{pk}}\ge {10}^{12}\mathrm{kg}$ whereas for the broad case the observed energy densities can be reproduced regardless of peak mass. Adopting some simplifications for the early-time expansion history as a first approximation, we also find that the measured baryon asymmetry can be recovered within an order of magnitude. We argue furthermore that the correct value of the baryon-lepton yield can in principle be retrieved for scenarios where a significant amount of the radiation is produced by PBH decay during or after reheating, as is expected when the decaying PBHs also cause reheating, or when an early matter-dominated phase is considered. We conclude from this first analysis that the model merits further investigation.

Figure 1

Polychromatic PBH mass spectrum (purple solid) and a monochromatic spectrum peaked at $M_{\mathrm{pk}}={10}^5\mathrm{kg}$ (blue dashed). The polychromatic spectrum is the envelope of many such monochromatic spectra which are produced at different collapse times. The green dashed line illustrates the behavior of the polychromatic spectrum at the high-mass end given by Eq. (5).

Figure 2

Evolution of the PBH mass parametrized by the scale factor $a$ (normalized to unity today). Different initial masses evaporate at different points in the evolution of the Universe.

Figure 3

Fractional energy densities for PBHs [top panel, Eq. (13)] and for baryons [bottom panel, Eq. (31)] for ${\psi }_{\mathrm{mono}}$ with various choices of peak masses. We tune ${\overline{n}}_0$ and $\lambda$ to match the Planck 2018 $\mathrm{\Lambda }\mathrm{CDM}$ mean values for ${\mathrm{\Omega }}_{\mathrm{CDM}}$ and ${\mathrm{\Omega }}_b$ at the time of recombination, $a_{\mathrm{CMB}}=9\times {10}^{-4}$, marked as a vertical dotted line. The $\mathrm{\Lambda }\mathrm{CDM}$ predictions for ${\mathrm{\Omega }}_{\mathrm{CDM}}$ and ${\mathrm{\Omega }}_{\mathrm{b}}$ are given by dashed black lines. The horizontal gray dotted lines indicate the observed proportions of total matter in the CDM and baryon fractions. The reheating temperature is taken to be $T_{\mathrm{RH}}={10}^8\mathrm{GeV}$.

Figure 4

The top panel shows the number density of PBHs at the time of recombination $n_{\mathrm{PBH},\mathrm{acmb}}$ as a function of peak mass $M_{\mathrm{pk}}$. The dotted line represents the geometrically maximally allowed number density for the mass spectrum at the time of recombination. The bottom panel shows the fractional energy density predicted for PBHs with ${\psi }_{\mathrm{mono}}$ at present day, ${\mathrm{\Omega }}_{\mathrm{PBH},0}$, using Eq. (13), as a function of peak mass $M_{\mathrm{pk}}$. We tune ${\overline{n}}_{\mathrm{PBH},0}$ to match the $\mathrm{\Lambda }\mathrm{CDM}$ prediction for ${\mathrm{\Omega }}_{\mathrm{CDM}}$ at the time of recombination as in Fig. 3. The dashed line represents the fractional energy density of CDM at present day according to Planck 2018.

Figure 5

The top panel shows the coupling constant $\lambda$ required to match predictions for ${\mathrm{\Omega }}_b$ to the observed fractional energy density of baryonic matter at the time of recombination as a function of the peak mass $M_{\mathrm{pk}}$ of ${\psi }_{\mathrm{mono}}$. The bottom panel shows the baryon-lepton yield $Y_{\mathrm{B}-\mathrm{L}}$ as a function of the scale factor $a$ for a reheating temperature in accordance with Eq. (14). The dotted vertical line corresponds to the scale factor at reheating time $a_{\mathrm{RH}}$ and the dashed horizontal line corresponds to the predicted yield at present day. The reheating temperature is taken to be $T_{\mathrm{RH}}={10}^8\mathrm{GeV}$.

Figure 6

Baryon-lepton yield $Y_{\mathrm{B}-\mathrm{L}}$ as a function of the ratio between the effective fractional radiation energy density extrapolated from early to present times ${\mathrm{\Omega }}_{\gamma ,\mathrm{eff}}$ and the observed fractional radiation energy density today ${\mathrm{\Omega }}_{\gamma ,0}$. If a significant amount of the radiation is produced by the decay of PBHs, ${\mathrm{\Omega }}_{\gamma ,\mathrm{eff}}\ll {\mathrm{\Omega }}_{\gamma ,0}$, as would for instance be expected if the decaying PBHs were to cause reheating, the model can reproduce the observed yield. The dotted and dashed lines are observational bounds for different assumptions (Appendix pp1-s2). The reheating temperature is taken to be $T_{\mathrm{RH}}={10}^8\mathrm{GeV}$.