The impact of Hawking radiation from primordial black holes on recombination and the Hubble tension

Technical Summary: The Impact of Hawking Radiation from Primordial Black Holes on Recombination and the Hubble Tension

Problem Statement
The paper addresses the "Hubble tension," a significant discrepancy (>5σ) between the present-day Hubble constant ($H_0$) inferred from early-universe Cosmic Microwave Background (CMB) observations ($H_0 \approx 67.4$ km s$^{-1}$ Mpc$^{-1}$) and local late-time measurements using the cosmic distance ladder ($H_0 \approx 73$ km s$^{-1}$ Mpc$^{-1}$). The authors investigate whether Primordial Black Holes (PBHs) evaporating via Hawking radiation during the epoch of recombination ($z \approx 1100$) could act as an additional ionization and heating source. Such heating would delay the recombination process, shifting the surface of last scattering to lower redshifts, which theoretically increases the inferred value of $H_0$ derived from CMB data.

Methodology
The authors utilized the recfast recombination code (version 1.5.0) to simulate the thermal and ionization history of the Universe. They modified the code to include energy injection from evaporating PBHs. Key methodological steps included:

• Ionization Mechanisms: The study focused on secondary ionization (heating via Compton scattering and pair-production) rather than direct photoionization, as the high-energy photons from PBHs ($E \sim 100$ MeV–GeV) have a low photoelectric cross-section. The authors assumed that all electromagnetic energy from evaporating PBHs is eventually deposited into the surrounding gas, though they noted that neutrino losses (approx. 40–50% of total luminosity) and grey body factors introduce significant uncertainties.
• PBH Population Models: Simulations were run with non-monochromatic Initial Mass Functions (IMFs) following power laws ($M^{-1}$ and $M^{-2}$) across a mass range of $10^{-20}$ to $10^{-17.5} M_\odot$. This range was selected because PBHs in this window evaporate entirely during or before recombination.
• Parameter Space: The fraction of dark matter in the form of PBHs ($f_{C,PBH}$ or $\Omega_{PBH}$) was varied from $10^{-6}$ to $10^{-2}$. The simulations calculated the resulting change in the ionization fraction ($\Delta x$) and the shift in the redshift of matter-radiation decoupling ($z_\star$).
• Hubble Constant Calculation: The shift in $z_\star$ was converted to a fractional change in $H_0$ using the relation $\Delta H_0/H_0 \approx \frac{3}{2} \Delta z / (1+z_\star)$.
• Constraints: The authors cross-referenced their results with existing constraints from the extragalactic gamma-ray background, positron annihilation (511 keV line), and Voyager 1 cosmic ray flux. They also used CAMB to check for observable signatures in the CMB power spectrum (specifically E-mode polarization).

Key Results

1. Impact on Recombination: PBH heating delays recombination. For a PBH density of $\Omega_{PBH} \approx 10^{-3} \Omega_C$ (with an $M^{-1}$ IMF), the redshift of the surface of last scattering shifts from $z_\star = 1081$ (standard $\Lambda$CDM) to $z_\star = 1017$.
2. Resolution of Hubble Tension: A PBH energy density of $\Omega_{PBH} \approx 10^{-3} \Omega_C$ yields an $\approx 8.9\%$ increase in $H_0$, which is sufficient to bridge the gap between Planck CMB data and local distance ladder measurements. Even lower densities ($\Omega_{PBH} \approx 10^{-4} \Omega_C$) produce changes ($>1.8\%$) larger than current measurement uncertainties.
3. IMF Sensitivity: The shape of the IMF is critical. An $M^{-2}$ IMF (biased toward lower masses) produces ionization boost factors approximately 6.4 times larger than an $M^{-1}$ IMF at the same total PBH density, because lower-mass PBHs evaporate more rapidly and earlier.
4. Upper Limits and Reionization:
   • Absolute Upper Limit: $\Omega_{PBH} < 10^{-2} \Omega_C$. Densities above this threshold cause a "secondary reionization," keeping the Universe ionized ($x_e \approx 1$) for extended periods after standard recombination, which contradicts CMB observations.
   • Mass Limits: PBHs with masses $> 10^{-17.5} M_\odot$ are constrained because they would evaporate and ionize the intergalactic medium at low redshifts ($z < 100$), inconsistent with Lyman-$\alpha$ forest data.
5. CMB Power Spectrum: While PBHs alter the ionization history, the resulting changes in the CMB E-mode polarization power spectrum (EE) are subtle. The root mean square difference between the highest ($10^{-2}$) and lowest ($10^{-5}$) PBH fractions is only $\approx 0.6\%$ of the peak signal, suggesting these effects might not have been definitively ruled out by Planck data alone.

Significance and Claims
The paper posits that evaporating PBHs represent a physically plausible, non-exotic mechanism to modify the early Universe's ionization history and potentially alleviate the Hubble tension. However, the authors maintain a cautious stance regarding the magnitude of this effect:

• Uncertainties: The precise correction to $H_0$ is hindered by "grey body factors" (dependent on unknown PBH spin and charge) and neutrino losses, which could alter the effective heating rate by a factor of two.
• Sensitivity: $H_0$ is extremely sensitive to $\Omega_{PBH}$. A slight increase in PBH density leads to a substantial change in the inferred expansion rate.
• Conclusion on the Tension: The authors argue that while PBHs alone are unlikely to resolve the entire tension (as shifting the sound horizon introduces other tensions with Baryon Acoustic Oscillations), they could contribute meaningfully.
• Recommendation: Until the non-gravitational properties of dark matter are better constrained, the authors suggest that the hypothesis that the Universe's ionization history strictly matches the standard thermal history of $\Lambda$CDM is "too precarious" to rely upon for determining $H_0$. Consequently, they suggest that measuring $H_0$ locally at $z \lesssim 1$ may currently be a more robust approach than inferring it from the CMB.