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.


I. INTRODUCTION
One of the most significant open questions in cosmology is how the universe came to contain more matter than antimatter. This asymmetry is typically characterized in terms of the dimensionless quantity: where n B and nB are the number densities of baryons and anti-baryons, respectively, and n γ = 2ζ(3)T 3 /π 2 is the number density of photons in a blackbody distribution of temperature, T . It is also sometimes useful to write this quantity in terms of the number density of baryons per unit entropy density: where g S ≈ 3.9 is the number of degrees-of-freedom in entropy at the universe's current temperature. Although the value of this quantity could, in principle, evolve with time, measurements of the cosmic microwave background (CMB) and the primordial light element abundances each yield Y B ≈ 8.8 × 10 −11 [1], indicating that any primordial abundance of antimatter had already disappeared by the onset of Big Bang nucleosynthesis (BBN). This, in turn, indicates that some mechanism must have driven the early universe to transition from a matter-antimatter symmetric state (with η = 0) at the end of inflation (or other initial condition), to one with an appreciable value of η. 1 While the nature of this mechanism remains unknown, it is well established that it must include each of the following elements, commonly known as the Sakarov conditions [3]: 1. Interactions which violate the conservation of baryon number.
2. Interactions which violate the symmetries of charge (C), and charge-parity (CP).
Many proposals have been put forward which satisfy these conditions and could potentially explain the existence of the observed baryon asymmetry. Some of the most well-known examples include electroweak baryogenesis [4][5][6][7][8][9][10][11], GUT baryogenesis [12][13][14][15][16][17], leptogenesis [18][19][20][21], and the Affleck-Dine mechanism [22,23]. Some of these ideas (namely leptogenesis and the Affleck-Dine mechanism) have not been significantly impacted by existing observations or experimental results, and remain as viable today as they were at the time of their proposal. In contrast, recent data has begun to place tension on many models of electroweak baryogenesis and GUT baryogenesis, in some cases even ruling out such scenarios.
Models of electroweak baryogenesis generally require the existence of relatively light particles in order to facilitate the necessary departure from thermal equilibrium. The lack of evidence for such particles at the Large Hadron Collider (LHC) significantly constrains this class of scenarios [24][25][26][27][28][29][30][31], typically requiring fine-tuning and/or large couplings which lead to Landau poles at scales not far above ∼ 1 TeV [32,33] (for potentially viable alternatives, see Refs. [34][35][36][37][38][39][40][41][42][43]). Meanwhile, theories of GUT baryogenesis have come under pressure from a very different direction, as a consequence of measurements of the CMB. In such scenarios, the baryon asymmetry is generated through the C, CP, and baryon number violating, out-of-equilibrium decays of very massive gauge or Higgs bosons in the very early universe. Although the precise mass of these exotic particles depends on the GUT gauge group and the representations under consideration, they are typically near the scale of GUT symmetry breaking. In supersymmetric SU (5), for example, the GUT gauge bosons (denoted by X and Y ) have masses of approximately M X,Y 10 16 GeV (in the absence of supersymmetry, GUTs based on SU (5) are ruled out by constraints on the proton lifetime) [44,45]. While the masses of the Higgs bosons found in GUTs are more sensitive to the choice of representation and other modeldependent considerations, the baryon number violating Higgs bosons in the simplest, 5-dimensional representation of SU (5) are typically taken to be M H ∼ 10 14 GeV or greater, an expectation that is additionally reinforced by constraints on proton decay.
In order for GUT baryogenesis to produce the observed baryon asymmetry, some combination of these very massive particles must have been copiously produced in the early universe. Constraints on the tensor-to-scalar ratio from Planck and the BICEP2/Keck Array, however, indicate that the energy scale of inflation was less than V 1/4 Inf < 1.6×10 16 GeV [46]. When this information is combined with the small magnitude of temperature fluctuations observed in the CMB, it suggests that the universe was reheated after inflation to a temperature of T < ∼ 10 9 − 10 13 GeV [46][47][48], well below the scale of grand unification, highly suppressing the thermal production of the baryon number and CP violating particles, and posing significant problems for many otherwise well-motivated theories of GUT baryogenesis. 2 Another challenge faced by many models of GUT baryogensis comes from the influence of sphalerons on any baryon asymmetry that might be produced. As soon as the temperature of the universe drops below T ∼ 10 12 GeV, sphaleron transitions rapidly drive the value of the net baryon-plus-lepton number (B + L) toward zero, erasing any asymmetry that may have been present at high temperatures [17]. The traditional way of avoiding this problem in GUT baryogenesis is for the particle decays to produce a non-zero value of B − L, which is not eroded by sphalerons. In many GUT models, however, such as those based on SU (5), no such net B − L is generated, leading to a situation in which the baryon asymmetry is efficiently washed out well before the electroweak phase transition.
It is within the context of these challenges for GUT baryogenesis that we consider the role that primordial black holes may have played in this process. This possibility has been discussed previously by a number of authors, in particular by Barrow et al. [54], and more recently in Refs. [55,56] (for other related work, see Refs. [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72]). In this study, we focus on the ways in which a population of primordial black holes could serve to relax some of the constraints and challenges that are otherwise faced in many baryogenesis scenarios based on GUTs. In particular, the presence of black holes in the early universe could have impacted the process of GUT baryogenesis in at least three separate and important ways: 1. Heavy Particle Production: As black holes undergo Hawking evaporation, their temperature increases. Thus even the heaviest of particles can be produced by black holes, regardless of the temperature of the universe after inflation.
2. Avoiding Washout: For any black holes heavier than ∼ (3 − 6) × 10 5 g (but lighter than ∼ 5 × 10 8 g in order to evade constraints from BBN [73,74]), the process of Hawking evaporation would be completed only after the electroweak phase transition, thereby automatically avoiding any problems with sphaleron washout.
3. Out of Equilibrium Decays: Any baryon number violating particles that are radiated from a black hole will be out-of-equilibrium with the thermal bath. Thus, their baryon number violating decays automatically satisfying the third Sakarkov condition, even if they decay promptly.
The remainder of this paper is structured as follows. In Sec. II, we review the formation, evolution, and evaporation of black holes in the early universe. We then briefly describe in Sec. III how baryon number is generated within the context of GUTs. In Sec. IV, we consider the role that black holes could play in GUT baryogenesis, calculating the magnitude of the baryon asymmetry that results in such scenarios. We then extend this discussion to the case of leptogenesis in Sec. V. Finally, we discuss and summarize our results in Sec. VI.

II. BLACK HOLES IN THE EARLY UNIVERSE
It has long been speculated that a significant abundance of black holes may have formed in the early universe [75,76], either as a consequence of inflation, or during a period involving a phase transition [65,77,78]. In particular, it has recently been argued that the production of black holes is a relatively generic prediction of simple, single-field inflation models [79,80].
Although the masses of any black holes formed in the early universe is model dependent, it is well motivated to consider values that are less than but comparable to the total energy enclosed within the horizon at the time of their formation [64,65,[81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97]: where M Pl = 1.22 × 10 19 GeV is the Planck mass, H is the Hubble rate, T is the temperature of radiation, and g (T ) is effective number of relativistic degrees-of-freedom. Thus for reheating temperatures of T ∼ 10 9 − 10 13 GeV [46][47][48], we should expect M BH ∼ (0.1 − 1)M hor ∼ 10 5 − 10 14 g. Black holes lose mass by radiating particles through the process of Hawking evaporation. In this study, we limit ourselves to the case of Schwarzschild black holes, which evaporate at the following rate [98]: where G ≈ 3.8 is the appropriate greybody factor, the temperature of a black hole is and the quantity g ,H (T BH ) counts the number of particle degrees-of-freedom with masses below ∼ T BH , according to the following prescription [99,100]: where w i = 2s i + 1 for massive particles of spin s i , w i = 2 for massless species with s i > 0, and w i = 1 for s i = 0. For T BH 10 2 GeV (M BH 10 11 g), the particle content of the Standard Model corresponds to g ,H 108. Alternatively, the full particle content of the Minimal Supersymmetric Standard Model (MSSM) corresponds to g ,H 316 [73].
It follows from Eq. (4) that a black hole will evaporate entirely over the following timescale: where M BH,i is the initial mass of the black hole and is the value of g ,H appropriately averaged over the course of the black hole's evaporation.
As the universe expands, the density of black holes evolves as matter, ρ BH ∝ a −3 , so the fraction of the total energy density in black holes grows proportionally to the scale factor during the era of radiation domination, ρ BH /ρ rad ∝ a −3 /a −4 = a [56,101,102]. More quantitatively, the total energy density of the early universe will become dominated by black holes before they finish evaporating if the following condition is satisfied: where ρ BH,i and ρ R,i represent the energy densities in black holes and radiation at an initial time when the radiation was at a temperature, T i . From this expression, it is clear that black holes could have dominated the total energy density of the early universe prior to their evaporation, even if their initial abundance was quite small. If the energy density of the universe was dominated by black holes at the time of their evaporation, the Hawking radiation would fill the universe with a hot bath of radiation, reheating the universe to a temperature, T RH . Under the approximation of instantaneous evaporation at t = τ BH , the temperature of this radiation can be calculated as follows: Applying Eq. (7) in the limit where g ,H is constant, and solving for T RH in Eq. (10), we obtain which should not be confused with the temperature of reheating following inflation. Throughout this paper, we will use T RH to denote the temperature of the universe following the evaporation of a black hole population, and will focus on black holes which evaporate before the onset of BBN (M BH,i < ∼ 5 × 10 8 g) [73,74].

III. THE GENERATION OF BARYON NUMBER IN GRAND UNIFIED THEORIES
A generic feature of GUTs are heavy bosons with baryon number violating couplings. For example, in SU (5) there are a total of 12 additional gauge bosons (denoted by X and Y ), each of which forms an SU (3) C triplet and SU (2) L doublet. The interactions of these particles connect quarks and leptons in a way that violates the conservation of baryon and lepton number, leading to processes such as p → π 0 e + . Although the precise rate at which GUT gauge bosons mediate proton decay is somewhat model dependent, a reasonable estimate is given by: where g GUT is the strength of the gauge coupling of the GUT force, and M X,Y are the masses of the gauge bosons mediating the decay. For g GUT ≈ 1/25 (the value at which the Standard Model gauge couplings unify in supersymmetric GUTs), the current constraint on proton decay from Super-Kamiokande of τ p /Br(p → π 0 e + ) < 1.67 × 10 34 years [103] allows us to restrict M X,Y > ∼ 3 × 10 15 GeV. Given that gauge coupling unification takes place at ∼ 10 16 GeV in supersymmetric SU (5), this class of models remains consistent with existing constraints on proton decay. In addition to the Higgs bosons that break the gauge symmetry of the GUT (which are contained in the adjoint representation of the GUT group), additional Higgs bosons are required to break electroweak symmetry at the weak scale, and to give masses to the Standard Model fermions. In SU (5), the minimal representation that can accommodate this is a 5 H or5 H (in supersymmetric GUTs, both 5 H and5 H Higgs multiplets are required in order to cancel anomalies) [104][105][106][107][108]. Each 5 H or5 H multiplet consists of an SU (2) doublet (such as that corresponding to a Higgs doublet near the electroweak scale) and a color triplet. Unlike the doublets, the Higgs triplets violate the conservation of both baryon and lepton number by coupling to the following combinations of Standard Model fermions (in each generation): ue − , dν, and ud [12]. Similar to those of the GUT gauge bosons, the interactions of the Higgs triplets lead to the following rate of proton decay: where M T is the mass of the Higgs triplet, and y u,d are its baryon and lepton number violating Yukawa couplings to first generation fermions. If the Higgs triplet has Yukawa couplings that are similar in magnitude to those of the electroweak Higgs doublet (y u,d ∼ O(m u /m t )), constraints from proton decay require that M T > ∼ 3 × 10 11 GeV.
In conventional GUT baryogenesis, the baryon asymmetry of the universe is generated through the baryon number violating (and C and CP violating) decays of X, Y , and T particles. The requirement that these particles be heavy enough to not induce an unacceptable rate of proton decay provides a challenge for this scenario, as the production of a large abundance of such particles in the early universe would appear to require a rather high reheating temperature. In the following section, we will consider an alternative scenario, in which the GUT bosons that generate the baryon asymmetry are produced at somewhat later times, through the Hawking evaporation of primordial black holes.

IV. THE ROLE OF BLACK HOLES IN GUT BARYOGENESIS
For black holes in the mass range under consideration in this study (M BH,i ∼ 10 0 − 10 9 g), their initial temperatures (T BH ∼ 10 4 − 10 13 GeV) are generally well below those required to radiate particles with GUT-scale masses. Consequently, Hawking evaporation only becomes capable of producing such massive particles once the black hole has already lost most of its mass, causing its temperature to become comparable to or greater than the mass of the particles in question. Here, we will focus on the Hawking radiation of Higgs triplets, which is efficient when T BH > ∼ M T . In this section, we calculate the quantities and average energies of the heavy particles produced through Hawking evaporation and use these results to obtain the baryon asymmetry that is generated when these particles decay in accordance with the Sakharov conditions. For future convenience, we define a the parameter which represents the average baryon yield per triplet decay in the limit where washout effects can be neglected; all of our results below will be proportional to this value. Here, the sum is over all final states, f , with net baryon number B f , and Γ T is the total width of the Higgs triplet. Note that in order for T = 0, one generally requires a second baryon number violating boson to be present in the loop-level decay diagrams. In the case of supersymmetric SU (5), this is naturally accommodated by the two Higgs Triplets that are contained within the 5 H and5 H representations.

A. The Kinematics of Black Hole Particle Production
Approximating that the average radiated triplet has an energy, E T ≈ 3T BH , we can estimate the number of Higgs triplets that are produced over the course of a black hole's lifetime: where g T H ≈ 6 × 1.82 ≈ 10.9 is the Hawking radiation weight per Higgs triplet (corresponding to 21.8 for the 5 H and 5 H Higgs representations required in supersymmetric GUTs), and g ,H 316 + g T H for the low-energy particle content associated with the MSSM. This result assumes that Higgs triplet production begins instantaneously (and without suppression) at T BH = M T .
A more careful result can be obtained by integrating over a Bose-Einstein distribution of radiated particles at temperature T BH . The rate of T production per unit black hole area can be written as where G is a greybody factor and the factor of 1/4 converts particle production per volume to production per area [70]. Integrating over the surface area, and applying Eqs. (4) and (5), the total rate of T production becomes where r s = 2M BH /M 2 Pl = (4πT BH ) −1 is the Schwarzschild radius, so the total number of triplets produced per black hole is In the limit of T BH,i M T , this reduces to while in the opposite limit (T BH,i M T ), we obtain the following: Similarly, the mass loss rate to T emission is so the total mass lost to T emission is and the average Lorentz boost per T particle weighted over the full BH lifetime is For relatively small values of M T and/or M BH , the average Lorentz factor could potentially be large, significantly delaying the decays of the Higgs triplets through time dilation. This will be the case, however, only if the Higgs triplets do not efficiently transfer their kinetic energy to the thermal bath though elastic scattering. The cross section for Triplet scattering with a gluon is given by σ T g→T g ∼ α 2 s T 2 /M 4 T , which is sufficiently large to establish kinetic equilibrium if the scattering rate exceeds the rate of Hubble expansion: where n g is the number density of gluons in the thermal bath and, in expression on the right, we have evaluated at the reheating temperature following an era of black hole domination, T RH . Across most of the parameter space in which the Higgs triplets are produced with large Lorentz factors, these particles are rapidly cooled through scattering with gluons, efficiently preventing any significant time dilation of their decays.

B. Baryogenesis From a Black Hole Dominated Era
In calculating the magnitude of the baryon asymmetry that is produced in the decays of the Higgs triplets radiated from black holes, we will first consider the case in which black holes dominated the energy density of the universe prior to their evaporation. Such an initial condition can be realized for any initial black hole energy density that satisfies the inequality in Eq. (9) and, once realized, is insensitive to any prior state of the early universe.
We begin by determining the number density of black holes at the time of their evaporation. From the definition of the Hubble rate in matter domination, we have where τ BH is given in Eq. (7). Note that the number density of black holes, n BH = ρ BH /M BH , at the time of evaporation is uniquely specified by the mass of the black holes. From this, the resulting baryon asymmetry from GUT Higgs triplet decays is where s is the entropy density at the time of evaporation, g S is the number of degrees-of-freedom in entropy, and N T from Eq. (18) is the number of triplets produced via Hawking radiation over the lifetime of a single black hole. Importantly, here T RH is the Standard Model radiation temperature that results entirely from Hawking radiation according to Eq. (11). Assuming triplets decay promptly, the baryon yield in the T BH,i M T limit is given by:  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.
For a fixed Y B , this relation which predicts a M T ∝ M

5/4
BH relationship, which corresponds to the scaling of the dashed contours in Fig. 1 for large values of M T in the upper left. In the T BH,i M T limit, we instead arrive at: which is independent of M T and corresponds to the vertical portions of the dashed contours in Fig. 1.
If M T > ∼ 3 × 10 11 GeV (as required by proton decay constraints, assuming that the Yukawa couplings of the Higgs triplet are equal in magnitude to those of the Higgs doublet), obtaining the measured baryon asymmetry requires [54][55][56] However, from Eq. (11), for black holes in this mass range, the process of Hawking evaporation ends when the temperature of the universe is well above that of the electroweak phase transition, enabling sphalerons to wash out any net value of B + L that was generated through the Higgs triplet decays. To avoid sphaleron washout, one could consider GUTs that are not based on SU (5) and that are capable of generating a net abundance of B − L, which remains conserved even at temperatures above the electroweak phase transition. This situation is summarized in Fig. 1.

C. Baryogenesis From a Subdominant Black Hole Population
One can obtain a more general solution for Y B by rescaling the value of T in Eqs. (27) and (28) by ρ BH /ρ tot , as evaluated at the time of evaporation. Unlike in those scenarios which included a black hole dominated era, the result in this case depends on the initial conditions and, more specifically, on the composition of the universe at the time of black hole formation.
We can write the baryon yield in this case as follows: where T τ is the temperature of the radiation bath and ρ BH /ρ tot | τ represents the ratio of these energy densities, each evaluated at the time of evaporation. As the universe expands, the fraction of the energy density in black holes grows linearly with the scale factor, so at evaporation we have where T i is the temperature of the radiation bath at the time of black hole formation and the temperature at evaporation is determined by the condition H = (2τ BH ) −1 , which yields In a case with no black hole dominated era, once again assuming that the triplets decay promptly, the baryon yield in the T BH,i M T limit is given by: Whereas in the T BH,i M T limit, we instead arrive at which is independent of M T as in the corresponding regime during black hole domination in Eq. (28).

D. Reducing The Yukawa Couplings of the Higgs Triplet
So far in this study, we have found that the observed baryon asymmetry, Y B ≈ 8.8×10 −11 , can be produced through the Hawking evaporation of baryon number violating Higgs triplets without inducing an unacceptable rate of proton decay only in scenarios with relatively light black holes, M BH < ∼ 5 × 10 2 g. Black holes in this mass range evaporate leaving the universe at a temperature well above the electroweak phase transition, enabling sphalerons to wash out any net value of B + L that may have been previously generated. One possible solution to this problem would be to consider GUTs which allow for the production of net B − L, which remains conserved at all temperatures. In this section, we will consider an alternative solution which involves reducing the Yukawa couplings of the Higgs triplet.
In the previous subsections, we assumed that the Yukawa couplings of the Higgs triplet are equal or similar in magnitude to those of the electroweak Higgs doublet. Given that the SU (3) triplet and SU (2) doublet are each part of the same 5 H or5 H multiplet, this is a reasonable and relatively minimal assumption. That being said, the large hierarchy between the mass of the Higgs triplet (as required by constraints from proton decay to be M T > ∼ 3×10 11 GeV) and the much smaller mass of the electroweak Higgs doublet would appear to involve an unacceptable degree of fine tuning, and this has motivated a great deal of model buliding, featuring a variety of potential solutions . Motivated by such considerations, we examine in this subsection scenarios in which the Yukawa couplings of the Higgs triplet are independent from those of the electroweak doublet, allowing us to consider much lower values of M T without inducing an unacceptable rate of proton decay. By suppressing the Yukawa couplings of the Higgs triplet, we find that it is possible to generate the observed baryon asymmetry from more massive black holes, which evaporate leaving the universe at a temperature below the electroweak phase transition, naturally avoiding the problem of sphaleron washout.
In the case of relatively light triplets, their annihilation rate can potentially exceed the rate of Hubble expansion, leading to the depletion of the triplet abundance before their decays can generate an appreciable baryon asymmetry. In the low-velocity limit, the cross section for triplet annihilation to gluons is given by the following: Excluded by BBN 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 considered 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.

FIG. 2. As in
The annihilation rate is the product of this cross section and the number density of triplets immediately after black hole evaporation, Γ T T →gg = σ T T →gg v n T = σ T T →gg v N T ρ(T BH )/M BH . Comparing this to the Hubble rate during radiation domination at a temperature T RH , we arrive at the condition for efficient triplet annihilation (evaluated in the T BH,i M T limit): The parameter space in this class of scenarios is summarized in Fig. 2, for the choice of Yukawa couplings which saturate the bound from proton decay. Throughout this study, whenever we alter the Yukawa couplings of the Higgs triplet, we simply rescale these quantities and parameterize this change in terms of their values relative to the constraints derived from proton decay. More specifically, we define where y DT denotes the values of the Yukawa couplings in the traditional case of doublet-triplet unification. In the following subsection, we will consider the case in which the Yukawas are even smaller (y y max ), leading to scenarios featuring long-lived Higgs triplets.

E. Long-Lived Triplets
Up to this point in the discussion, we have treated the decays of the Higgs triplets as instantaneous. This is a good approximation so long as the decay rate is rapid compared to the rate of Hubble expansion at the time. The width of the Higgs triplet is approximately given as [12]: Excluded by BBN 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 A 1). While the diagonal contours of constant YB are naively similar to those shown in Fig. 2, the underlying physics is quite different (see Appendix A 2). Furthermore, where the contours of constant YB = 8.8 × 10 −11 extend horizontally, the triplets do not only dominate the energy density, but dominate it by a factor greater than Y −1 B , leading to the generation of a baryon asymmetry that is independent of the mass of the black holes (see Appendix A 3).

FIG. 3. As in
where y t,b are the Yukawa couplings of the Higgs triplet to third generation quarks. If we set the magnitude of these Yukawa couplings such that they saturate the bounds from proton decay, y t,b < ∼ M T /(3 × 10 11 GeV), we arrive at: In the period of time after the completion of black hole evaporation, but before the decay of the triplets, the fraction of the total energy density consisting of non-relativistic triplets will increase by a factor of (a decay /a evap ) ≈ (τ T /τ BH ) 1/2 . Furthermore, if τ T > ∼ τ BH × (g ,H /g T ,H ) 2 , the Higgs triplet population will dominate the total energy density of the universe before they decay, potentially altering the results of our calculation. For example, if we take the Yukawa couplings of the triplet to be eight orders of magnitude smaller than the maximum value consistent with the constraints from proton decay, y = 10 −8 y max , a triplet-dominated era will occur if M T < ∼ 10 8 GeV × (10 6 g/M BH ). This case is illustrated in Fig. 3, where the contours of constant Y B = 8.8 × 10 −11 extend diagonally to the lowerright, until M T 1.4 × 10 2 × −2 T , at which point we enter a regime in which the triplets do not only dominate the energy density, but dominate it by a factor greater than Y −1 B . In this later limit, the resulting baryon asymmetry is independent of the mass of the black holes.

V. APPLICATION TO LEPTOGENESIS
In leptogenesis, a lepton number asymmetry is generated through the decays of right-handed neutrinos, which is then converted into a baryon asymmetry through processes involving sphalerons. If black holes are present and evaporating in the early universe, they could radiate these right-handed neutrinos, generating an asymmetry in a similar fashion to that described in the previous section. There are some key differences, however, between leptogenesis and baryogenesis within this context. In particular: 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 than that of the electroweak phase transition, making it impossible for sphalerons to convert the lepton asymmetry into a baryon asymmetry. Black holes lighter than MBH,i < ∼ 3 × 10 5 g could easily generate the observed baryon asymmetry through the Hawking radiation of lepton number violating right-handed neutrinos.
• The right-handed neutrinos do not induce proton decay, and thus are free to be relatively light, unlike GUT Higgs and gauge bosons.
• Due to its scalar nature, the contribution to g ,H from the Higgs triplet is somewhat enhanced relative to that from right-handed neutrinos (by a factor of 1.82 per degree-of-freedom).
In Fig. 4, we summarize the parameter space in which black holes can generate the baryon asymmetry through the lepton-number violating decays of right-handed neutrinos. Here, we have considered three generations of righthanded neutrinos of mass, M N . Black holes lighter than M BH,i < ∼ 3 × 10 5 g could easily generate the observed baryon asymmetry in this class of scenarios.
Lastly, we will comment that whereas constrains from the CMB and proton decay have ruled out or tightly constrained many models of GUT baryogenesis (thus motivating a role for black holes, as discussed in this paper), leptogenesis models have generally not been impacted by such constraints and remain broadly viable. From this perspective, the presence of primordial black holes does not seem to be a necessary (or even helpful) feature for leptogenesis.

VI. DISCUSSION AND SUMMARY
A significant abundance of black holes may have been formed in the early universe, either as a consequence of inflation or in subsequent phase transitions. Given that the energy density of black holes evolves as matter rather than radiation, their fractional abundance will increase as the universe expands, until they evaporate through the emission of Hawking radiation. From this perspective, it is well motivated to consider scenarios in which the total energy density of the early universe was dominated by black holes prior to their evaporation. Such black holes could potentially have played an important role in establishing the current composition of the universe. In particular, it has been argued that the Hawking evaporation of primordial black holes may have produced the universe's dark matter abundance [56,72,101,102,135,136], an observable density of dark radiation [102,136,137], or even a stochastic background of high-frequency gravitational waves [137,138]. In this paper, we have considered the possibility that the baryon asymmetry of the universe may have been generated through the Hawking evaporation of black holes (see also, Refs. [54][55][56]), focusing the mechanism of GUT baryogenesis.
In Grand Unified Theories (GUTs), a net baryon abundance can be generated through the out-of-equilibrium decays of gauge or Higgs bosons, whose couplings violate the conservation of CP and baryon number. In standard GUT baryogenesis, these particles are generated in the very early universe, at temperatures not far below the GUT scale. Recent constraints on the scale of inflation and the subsequent temperature of reheating, however, have begun to put pressure on this class of scenarios. In contrast, black holes could produce such particles through Hawking evaporation at significantly later times, regardless of the masses of the particles or the temperature of the early universe. Furthermore, by producing the baryon number violating particles through Hawking evaporation, the decays of these particles will automatically occur when they are out-of-equilibrium with the thermal bath, naturally satisfying Sakarkov's third condition.
In typical GUTs, the baryon-number violating Higgs color triplet is taken to be very heavy, with a mass not far below the GUT-scale. In this study, we have also considered the possibility that the Yukawa couplings of the Higgs triplet could be suppressed, allowing these particles to be relatively light without inducing an unacceptable rate of proton decay. In this class of scenarios, and for black holes with masses in the range of M BH ∼ 10 5 − 10 9 g, the baryon asymmetry could be generated after the electroweak phase transition, naturally evading the effects of sphalerons which would ordinarily wash out any net baryon-plus-lepton number that was produced at early times. We have also identified interesting regions of parameter space in which the Higgs triplets can be long-lived, and come to dominate the energy density of the universe prior to their decays.