Assessing the tension between a black hole dominated early universe and leptogenesis

We perform the first numerical calculation of the interplay between thermal and black hole induced leptogenesis, demonstrating that the right-handed neutrino surplus produced during the evaporation only partially mitigates the entropy dilution suffered by the thermal component. As such, the intermediate-mass regime of the right-handed neutrinos, ${10}^6\mathrm{GeV}\lesssim M_N\lesssim {10}^9\mathrm{GeV}$, could not explain the observed baryon asymmetry even for fine-tuned scenarios if there existed a primordial black hole dominated era, consistent with initial black hole masses of $M_i\gtrsim \mathcal{O}(1)\mathrm{kg}$ and initial energy density fractions larger than ${\beta }^{\prime }\gtrsim {10}^{-6}$. A possible detection of the gravitational waves emitted from the same primordial black holes would place intermediate-scale thermal leptogenesis under tension. https://github.com/earlyuniverse/ulysses

Figure 1

An example solution of the full $\mathrm{Boltzmann}+\mathrm{PBH}$ system of equations for $M_i=7\mathrm{g}$, ${\beta }^{\prime }={10}^{-3}$, and $M_{N_1}={10}^{10}\mathrm{GeV}$. The left plot shows the evolution of energy densities of the black holes (black) and radiation (orange) as a function of $z=M_{N_1}/T$. The right plot shows the evolution of the magnitude of right-handed neutrinos normalized to the initial photon density (blue) and the magnitude of the baryon-to-photon ratio (Tyrian purple) as a function of $z$, including PBHs (full lines) and the standard—without PBHs—scenario (dashed lines).

Figure 2

The final baryon-to-photon ratio as a function of the initial black hole masses for varying masses of the RH neutrino. The grey dotted line shows the measured baryon-to-photon ratio [25] while the color dashed lines indicate the result obtained from leptogenesis in the case that there was no PBH dominated era. In both plots we assume ${\beta }^{\prime }={10}^{-3}$.

Figure 3

$|{\eta }_{\mathrm{B}}|$ as function of the initial fraction ${\beta }^{\prime }$ and PBH mass $M_i$ for two different benchmarks, $M_{N_1}={10}^{11}\mathrm{GeV}$ (left) and $M_{N_1}={10}^8\mathrm{GeV}$ (right). The white line indicates the values from which it is expected an early PBH dominated era.

Figure 4

Stochastic gravitational wave spectrum generated by evaporating primordial black holes.

Figure 5

The left plot shows the evolution of energy densities of the black holes (black) and radiation (yellow) as a function of the logarithm of the scale factor for the before scenario. The central plot shows the evolution of the magnitude of right-handed neutrino and flavored components of the lepton asymmetry comoving number densities as a function of the logarithm of $z=M_N/T$. The right panel presents the magnitude of the baryon-to-photon ratio as a function of the logarithm of $z$.

Figure 6

The analogous plots for the during scenario.

Figure 7

The analogous plots for the after scenario.