GUT baryogenesis with primordial black holes

In models of baryogenesis based on grand unified theories (GUTs), the baryon asymmetry of the Universe is generated through the $CP$ and baryon number violating, out-of-equilibrium decays of very massive gauge or Higgs bosons in the very early Universe. Recent constraints on the scale of inflation and the subsequent temperature of reheating, however, have put pressure on many such models. In this paper, we consider the role that primordial black holes may have played in the process of GUT baryogenesis. Through Hawking evaporation, black holes can efficiently generate GUT Higgs or gauge bosons, regardless of the masses of these particles or the temperature of the early Universe. Furthermore, in significant regions of parameter space, the black holes evaporate after the electroweak phase transition, naturally evading the problem of sphaleron washout that is normally encountered in GUT models based on $SU(5)$. We identify a wide range of scenarios in which black holes could facilitate the generation of the baryon asymmetry through the production and decays of GUT bosons.

Figure 1

Parameter space for producing the observed baryon asymmetry as a function of $M_{\mathcal{T}}$ and $M_{\mathrm{BH}}$. The dashed curves represent regions where $Y_B=8.8\times {10}^{-11}$, for various values of ${\epsilon }_{\mathcal{T}}$. In this figure, we have assumed that black holes dominated the energy density of the Universe prior to their evaporation, and we have taken a common value for Yukawa couplings of the Higgs (electroweak) doublet and (color) triplet. In the region not excluded by proton decay constraints, the Universe is reheated by black hole evaporation to a temperature greater than that of the electroweak phase transition, enabling sphalerons to wash out any net value of $B+L$ that was generated through the decays of Higgs triplets. To avoid sphaleron washout, one could consider GUTs that are not based on $SU(5)$, which in some cases can be capable of generating a net $B-L$, which remains conserved even at temperatures above the electroweak phase transition.

Figure 2

As in Fig. 1, but rescaling the Yukawa couplings of the Higgs triplet such that they saturate the constraint from proton decay. By suppressing the Yukawa couplings of the Higgs triplet, we find that it is possible to generate the observed baryon asymmetry with black holes of much larger mass, which evaporate after the electroweak phase transition. In the blue region, the triplets decay prior to the electroweak phase transition, enabling sphalerons to wash out any net value of $B+L$ that was generated through the Higgs triplet decays (the baryon asymmetry can only be generated in this parameter space if one considers GUTs which are capable of generating a net value of $B-L$). In the white region, any baryon asymmetry that is produced through triplet decays is protected from the effects of sphaleron washout. In the red region, the annihilation rate of the triplets exceeds that of Hubble expansion, leading to the depletion of the triplet abundance before an appreciable baryon asymmetry can be generated. Throughout this figure, we have assumed that black holes dominate the energy density of the Universe prior to their evaporation.

Figure 3

As in Fig. 2, but setting the Yukawa couplings of the Higgs triplet to ${10}^{-8}$ times the maximum value consistent with the constraints from proton decay. By suppressing these Yukawa couplings, the triplets become long-lived, leading to an era in which the triplets dominate the energy density of the Universe prior to their decay (see Appendix pp1-s1). While the diagonal contours of constant $Y_B$ are naively similar to those shown in Fig. 2, the underlying physics is quite different (see Appendix pp1-s2). Furthermore, where the contours of constant $Y_B=8.8\times {10}^{-11}$ extend horizontally, the triplets not only dominate the energy density, but they dominate it by a factor greater than $Y_B^{-1}$, leading to the generation of a baryon asymmetry that is independent of the mass of the black holes (see Appendix pp1-s3).

Figure 4

As in the previous figures, but for the case of leptogenesis. The dashed lines represent values of the right-handed neutrino mass and initial black hole mass that generate the observed baryon asymmetry, for various values of ${\epsilon }_N$. In this figure, we have assumed that black holes dominated the energy density of the Universe prior to their evaporation. In the red region, the Universe is reheated by black hole evaporation to a temperature below that of the electroweak phase transition, making it impossible for sphalerons to convert the lepton asymmetry into a baryon asymmetry. Black holes lighter than $M_{\mathrm{BH},i}\lesssim 3\times {10}^5\mathrm{g}$ could easily generate the observed baryon asymmetry through the Hawking radiation of lepton number violating right-handed neutrinos.