Can a Breakdown of Hawking Evaporation Open a New Mass Window for Primordial Black Holes as Dark Matter?

Abstract

Semi-classical Hawking evaporation is expected to break down at some point in a black hole's evolution as the effects of quantum gravity become important. In particular, it has been argued that the so-called memory-burden effect could cause black holes to become stabilized by the information that they carry, thereby suppressing the rate at which they undergo Hawking evaporation. It has furthermore been suggested that this opens a new mass window, between $10^{4}\,{\rm g} \lesssim M \lesssim 10^{10}\,{\rm g}$, over which primordial black holes could constitute the dark matter of our Universe. We show for the first time that this is true only if the transition from the semi-classical phase of a black hole to its memory-burdened phase is practically instantaneous. If this transition is instead more continuous, Hawking evaporation will persist at relevant levels throughout the eras of Big Bang Nucleosynthesis and recombination, leading to stringent constraints which rule out the possibility that black holes lighter than $\sim 4 \times 10^{16}\,{\rm g}$ could make up all or most of the dark matter. More broadly, our analysis demonstrates that even if departures from the semi-classical Hawking evaporation occur as proposed, they must be both drastic and abrupt to open viable new mass windows for primordial black hole dark matter.

Figures (6)

• Figure 1: The evaporation rate of a black hole with an initial mass of $M_{i} = 10^{6}\,\mathrm{g}$ (corresponding to a semi-classical evaporation time of $t_{\rm evap} \sim 4 \times 10^{-10}\,\mathrm{s}$) as a function of the remaining mass fraction, $M/M_{i}$. The black curve represents the semi-classical approximation (see Eq. \ref{['eq:SC']}), while the red curve depicts the step-like memory burden approximation, (see Eq. \ref{['eq:stepMB']}), corresponding to the case of $q = 0.5$ and $\delta = 0$. The blue curves show several examples of a smooth transition between the semi-classical and memory-burdened phases, for selected choices of $q$ and $\delta$ (see Eq. \ref{['eq:smooth_MB']}). Here, we have adopted $k=2$.
• Figure 2: The time profile of the Hawking radiation from a black hole with an initial mass of $M_{i} =10^{6}\,\mathrm{g}$ (corresponding to a semi-classical evaporation time of $t_{\rm evap} \sim 4\times 10^{-10}\,\mathrm{s}$). The black curve represents the semi-classical approximation (see Eq. \ref{['eq:SC']}), while the red curve depicts the step-like memory burden approximation (see Eq. \ref{['eq:stepMB']}), corresponding to $q = 0.5$ and $\delta = 0$. The blue curves represent the profile for the continuous parameterization of Eq. \ref{['eq:smooth_MB']}, for several values of $q$ and $\delta$. Here, we have adopted $k=2$.
• Figure 3: Upper limits on the abundance of primordial black holes as a function of their initial mass, shown for several values of $q$ and $\delta$. Constraints are derived from both the primordial light element abundances (green) and CMB anisotropies (blue). The gray region corresponds to primordial black holes that would have fully evaporated by now. The quantity, $f_{{\rm PBH},0}$, is the initial fraction of the dark matter that consists of primordial black holes. The thick solid black line highlights the bounds for a step-like memory-burden transition $(q = 0.5,\,\delta = 0)$, which would leave a relatively large mass window unconstrained, $10^{4} \, {\rm g} $<$ $\sim$ ~ M_i $<$ $\sim$ ~ 10^{10} \, {\rm g}$Alexandre:2024nuoDvali:2024hsbThoss:2024hsr. As we have shown here, however, if there is a continuous transition between the semi-classical and memory-burdened phases of a black hole's evolution ($\delta>0$), this window closes due to the strong constraints from both BBN and the CMB. Here, we have adopted $k=2$.
• Figure 4: Upper limits on the abundance of primordial black holes as a function of their initial mass, shown for four small values of $\delta$. In the limit $\delta\rightarrow 0$, we recover the results of the step-like memory burden approximation. Constraints are derived from both the primordial light element abundances (green) and CMB anisotropies (blue), highlighting how a continuous transition to the memory-burden phase affects these bounds. The gray region corresponds to primordial black holes that would have fully evaporated within the age of the Universe. Here, we have adopted $q=0.8$ and $k=2$, with $f_{{\rm PBH},0}$ denoting the initial fraction of the dark matter that consists of primordial black holes.
• Figure 5: As in Fig. \ref{['fig:results_3']}, but for three values of $k$. From this comparison, we see that this parameter choice has little impact on the resulting bounds. Here, we have adopted $q=0.8$ and $\delta=0.1$.