Baryogenesis from Exploding Primordial Black Holes

Abstract

Exploding primordial black holes can source baryon asymmetry soon after the electroweak phase transition, as high-energy Hawking radiation drives ultrarelativistic shocks in the surrounding plasma. The shocks and their trailing rarefaction waves delineate two bubble-like walls around a shell of superheated fluid, in which electroweak symmetry is restored. These moving interfaces source chiral charge, which is converted to baryon number. Upon adding a simple CP-violating operator at the TeV scale, this mechanism yields the observed baryon asymmetry with minimal dependence on PBH model parameters.

Figures (7)

• Figure 1: A schematic of the baryogenesis mechanism. (Left) Constant emission from a PBH of mass $M>M_{\rm thres}$ heats the plasma and establishes a quasi-steady-state temperature profile. (Center) The PBH explodes. Instantaneous energy injection when the PBH has remaining mass $M_{\rm thres}$ creates a fireball of superheated plasma. (Right) The over-pressured region expands outward as an ultrarelativistic blast wave. The shock front and trailing rarefaction wave enclose a thin shell of fluid with $T>T_{\rm EW}$, where EW symmetry is restored.
• Figure 2: ( Left) Plot of the BAU yield of Eq. (\ref{['Ydef']}) as a function of $\bar{M}$ given some $\alpha$ and $\beta$, with $\kappa_i=10^{-8}$ and $K = 5$ fixed. ( Right) Maximum BAU yield as a function of $\kappa_i$ for critical collapse parameters $\alpha = \beta = 2.78$. The vertical line shows the average value of $\bar{\kappa}$ for the six simulations (black points), as defined in Appendix \ref{['sec:MonoLim']}. For values of the initial PBH fraction $\kappa_i\ll\bar{\kappa}$, the early universe remains radiation-dominated, while $\kappa_i\gg\bar{\kappa}$ introduces a brief, transient period of PBH matter domination prior to BBN. The maximum yield saturates for $\kappa_i\gg\bar{\kappa}$ due to entropy injection.
• Figure A1: ( Left) Baryon number produced at the symmetry-restoring wall (shock front) as a function of the wall velocity $v_w$. ( Right) Baryon number produced at the symmetry-breaking wall (rarefaction wave) as a function of the wall velocity $v_w$. We consider representative values of shock front wall thickness, $L_{\rm w} = [1,5]/T_{\rm b}$.
• Figure A2: Evolution of the comoving PBH energy density $\rho_{\rm PBH}^{\rm co}(t)/\rho_{{\rm PBH},i}^{\rm co}$ for three sets of model parameters with $\bar{M}=10^{5.7} \, {\rm g}$ fixed. The typical lifetime $\tau(\bar{M})$ is indicated with a vertical gray line.
• Figure A3: Results from numerically solving the system of four evolution equations with representative model parameters $\alpha=\beta=2.78$, $\bar{M}=10^{5.7}\, {\rm g}$, and initial PBH density fraction $\kappa_i = 10^{-8}$, which admit a transient period of PBH matter domination. PBHs with this initial number distribution function would form at time $1.7\times10^{-32}\,{\rm s}$. Most PBHs would explode by time $\tau(\bar{M})=5.2\times10^{-11}\, {\rm s}$ (leftmost vertical gray line), and all but one in $10^{10}$ would have exploded by time $t_{\rm cut}$ (rightmost vertical gray line).