Primordial regular black holes as all the dark matter. III. Covariant canonical quantum gravity models

TL;DR

This paper investigates whether primordial regular black holes (PRBHs) can make up all dark matter within a covariant canonical quantum gravity framework by focusing on the Zhang-Lewandowski-Ma-Yang (ZLMY) regular BH. The analysis combines covariant effective QG with Hawking radiation: GBFs are computed via the Teukolsky equation using GrayHawk, Hawking spectra are derived from the ZLMY temperature $T(\xi)$, and the present-day photon flux is confronted with the diffuse gamma-ray background to bound the PBH fraction $f_{\text{pbh}}$ in the mass range $10^{15}-10^{18}$ g. A key result is that $T(\xi) > T_{\text{Sch}}$ for $\xi \neq 0$, with up to a $\sim 1.25$-fold increase, which strengthens evaporation signals and tightens constraints, pushing the asteroid-mass DM window to higher masses (e.g. $M_{\text{pbh}} \sim 2\times 10^{17}$ g for $\xi/M=3$). This demonstrates that enforcing general covariance in quantum gravity not only cures singularities but also materially changes observational predictions for PBH DM.

Abstract

In earlier companion papers, we showed that non-singular primordial black holes (PBHs) could account for all the dark matter (DM) over a significantly wider mass range compared to Schwarzschild PBHs. Those studies, mostly based on phenomenological metrics, are now extended by considering the quantum-corrected space-time recently proposed by Zhang, Lewandowski, Ma and Yang (ZLMY), derived from an effective canonical (loop) quantum gravity approach explicitly enforcing general covariance. Unlike the BHs considered earlier, ZLMY BHs are free from Cauchy horizons, and are hotter than their Schwarzschild counterparts. We show that this higher temperature boosts the evaporation spectra of ZLMY PBHs, tightening limits on their abundance relative to Schwarzschild PBHs and shrinking the asteroid mass window where they can constitute all the DM, a result which reverses the earlier trend, but rests on firmer theoretical ground. While stressing the potential key role of quantum gravity effects in addressing the singularity and DM problems, our study shows that working within a consistent theoretical framework can strongly affect observational predictions.

Figures (4)

• Figure 1: Evolution of the Zhang-Lewandowski-Ma-Yang BH temperature as a function of the regularizing parameter $\xi$, in units of mass $M$. The temperature is normalized by that of a Schwarzschild BH of the same mass, $T_{\text{Sch}}=1/8\pi M$. While the temperature is not a monotonically increasing function of $\xi$, it is always larger than the temperature of a Schwarzschild BH of the same mass.
• Figure 2: Graybody factor $\Gamma_{l=1}^{s=1}$ as a function of $\omega M$ for Schwarzschild BHs (blue solid curve) and Zhang-Lewandowski-Ma-Yang regular BHs (magenta dash-dotted curve). For illustrative purposes, we only plot $\Gamma_{l=1}^{s=1}$, since we are interested in photons ($s=1$) and the dominant emission mode is the $l=1$ one, while fixing the regularizing parameter to $\xi/M=3$. We see that the Zhang-Lewandowski-Ma-Yang GBF is consistently higher than the Schwarzschild one, and starts rising at much lower energies. The features shown in this plot do not change sensibly for higher values of $l$ and other values of $\xi$.
• Figure 3: Primary photon spectra resulting from the evaporation of a primordial regular Zhang-Lewandowski-Ma-Yang BH of mass $10^{16}\,{\text{g}}$ for different values of the regularizing parameter $\xi$ (normalized by the mass $M$): $\xi/M=1$ (red dotted curve), $2$ (green dashed curve), and $3$ (magenta dash-dotted curve). The blue solid curve corresponds to the case $\xi/M=0$, which recovers the Schwarzschild BH.
• Figure 4: Upper limits on $f_{\text{pbh}}$, the fraction of dark matter in the form of primordial regular Zhang-Lewandowski-Ma-Yang BHs, as a function of the PBH mass $M_{\text{pbh}}$. The limits are derived for different values of the regularizing parameter $\xi$ (normalized by the mass $M$), with the shaded regions excluded: $\xi/M=1$ (red dotted curve), $2$ (green dashed curve), and $3$ (magenta dash-dotted curve). Note that the blue solid curve corresponds to the case $\xi/M=0$, which recovers the Schwarzschild BH, whereas the value of $M_{\text{pbh}}$ corresponding to the upper right edge of the $f_{\text{pbh}}$ constraints marks the lower edge of the asteroid mass window.