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REVIEW 4 major objections 6 minor 68 references

The paper argues that primordial black holes carrying only ~0.1% of the dark matter density could delay recombination enough to raise the CMB-inferred Hubble constant by ~8.9%, nominally resolving the Hubble tension.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-01 15:08 UTC pith:ERHGU3A5

load-bearing objection The headline '8.9% resolves the Hubble tension' is an artifact of a degenerate Δz→H0 mapping, not a robust prediction—but the forward Recfast calculation and public code are a legitimate, useful contribution. the 4 major comments →

arxiv 2607.18528 v1 pith:ERHGU3A5 submitted 2026-07-20 astro-ph.CO

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

Adam Batten , Jeremy Mould This is my paper
classification astro-ph.CO
keywords primordial black holesHawking radiationrecombinationHubble tensioncosmic microwave backgroundionization historydark matter
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper asks whether Hawking radiation from primordial black holes (PBHs) could alter the recombination history of the early universe enough to change the value of the Hubble constant inferred from the cosmic microwave background. The authors simulate recombination with an added ionisation source from evaporating PBHs of mass ~10^-18 solar masses, and find that a PBH energy density of about 10^-3 of the cold dark matter density shifts the surface of last scattering from z*≈1081 to z*≈1017. Translated through a simple redshift-to-Hubble mapping, that delay corresponds to an 8.9% increase in H0, which would nominally eliminate the discrepancy between early- and late-time measurements. They also show that PBH fractions above ~10^-2 of the dark matter would reionise the universe at recombination, placing an upper limit on the allowed abundance. However, when they fit the CMB power spectrum with a Markov-chain Monte Carlo, the preferred PBH fraction is lower and the tension is not fully relieved, leading them to recommend local distance measurements as a more robust route to H0.

Core claim

Central claim: ~10^-18 solar-mass PBHs at 10^-3 of the dark matter density delay recombination by Δz≈64, translating to an 8.9% rise in the CMB-inferred H0. A fully evaporated PBH heats its surrounding gas independently of mass; abundance above 10^-2 would fully reionise at recombination. The 8.9% is nominal: grey-body factors and full CMB fitting lower the required fraction, leaving the tension not fully relieved.

What carries the argument

The key mechanism is the 'ionisation boost factor' Δx_H: the number of extra ionisations per atom produced by PBH evaporation, computed from energy conservation (Hawking mass-loss rate deposited into the gas) and integrated over a power-law mass function. The boost is added to a recombination code's ionisation equations at each redshift step, and the shifted last-scattering redshift z* feeds the analytic mapping ΔH0/H0 = (3/2) Δz/(1+z*). Secondary ionisation via Compton scattering and pair production is the dominant deposition channel, and grey-body factors modulate the Hawking spectrum.

Load-bearing premise

The central claim assumes that a delay in recombination translates one-for-one into a higher present-day Hubble constant, with the universe's matter density and other cosmological parameters held fixed, rather than the CMB actually constraining a combination that can be fitted by changing those parameters.

What would settle it

Measure the acoustic angle θ* = r_s/D_A from high-precision CMB temperature and polarization data. The paper's appendix shows that an 8.9% increase in h can be nearly nulled by a ~10% decrease in Ω_m; if a joint fit that includes PBH heating and lets Ω_m vary yields a shifted z* but an unchanged θ* and hence an unchanged H0, the 8.9% claim is refuted.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If PBHs at ~10^-3 of the dark matter density exist, the CMB-derived H0 would be ~8.9% higher, enough to overlap the local distance-ladder value and nominally resolve the tension.
  • PBH fractions above ~10^-2 of the dark matter are excluded because they would keep the universe ionised through recombination, contradicting the observed CMB.
  • Even a PBH fraction of 10^-4 of the dark matter shifts H0 by ~1.8%, larger than the current measurement uncertainties of both CMB and local distance-ladder determinations.
  • Because the heating from a fully evaporated PBH is independent of its mass, the effect scales simply with the total PBH fraction, making the qualitative prediction robust across different mass functions.
  • The authors conclude that measuring H0 locally at z≲1 is more robust than CMB inference until evaporating PBH populations are excluded.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The 8.9% resolution hinges on the assumption that the CMB constraint is on the recombination redshift z* rather than on the acoustic angle θ*; as the paper's own appendix shows, an increase in h can be nulled by a decrease in Ω_m, so a joint fit may shrink the effective H0 shift even if the ionization history is correct.
  • The grey-body factor uncertainty quoted as ranging from 0.1% to unity means the required PBH fraction is not tightly pinned down; a theoretical calculation or measurement of typical PBH spin and charge would sharpen or weaken the claimed resolution.
  • The same secondary-ionisation machinery could apply to other decaying or annihilating dark matter candidates; the finding that even a 10^-4 fraction leaves a detectable imprint suggests any non-standard ionisation source must be tightly constrained before H0 can be trusted from the CMB.
  • If the proposed shift is real, it should appear as a small but coherent change in the CMB damping tail and in the high-multipole EE polarization spectrum; suitably precise data could test the model independently of the Hubble-constant mapping.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper investigates whether Hawking radiation from primordial black holes (PBHs) in the mass range 10^-20–10^-17.5 M_sun can delay recombination and thereby raise the CMB-inferred Hubble constant. Using a modified Recfast recombination code, the authors compute ionization histories for a grid of PBH fractions and IMF slopes, then translate the shift in the last-scattering redshift z* into a fractional change in H0 via Eq. (3.3). They find that a PBH energy density ΩPBH ≈ 10^-3 ΩC with a M^-1 IMF delays last scattering by Δz ≈ 64, corresponding to ΔH0/H0 = 8.9%, which they state is enough to 'entirely reduce' the Hubble tension. They also derive an upper limit ΩPBH < 10^-2 ΩC and discuss constraints from the extragalactic gamma-ray background, the 511 keV line, and Voyager 1. An appendix includes a MCMC fit to ACT EE data that yields lower f_PBH and leaves the tension not fully relieved.

Significance. If the forward recombination calculations are taken at face value, the paper identifies a physically motivated mechanism—small evaporating PBHs—that can shift the recombination epoch, and it provides a public code and explicit caveats. The forward Recfast simulations are not circular and the paper is transparent about several limitations. However, the headline quantitative claim is not robust: the mapping from Δz to ΔH0 ignores the actual CMB observable (the acoustic angle), the energy deposition is overestimated by neglecting neutrino losses and tabulated deposition efficiencies, and the grey-body factor is an unconstrained multiplier. The paper's own appendices A.3 and A.4 undermine the abstract's strong claim. The work is useful as an exploratory study but needs substantial revision before the quantitative conclusions can be accepted.

major comments (4)
  1. [§3.2, Eq. (3.3), §A.1–A.3] The 8.9% headline rests on Eq. (3.3), whose derivation in A.1–A.2 assumes the CMB-inferred H0 is determined by H(z*) with all other parameters fixed. This is not how CMB experiments constrain H0: they measure the acoustic scale θ* = r_s/D_A. Appendix A.3 explicitly shows that an increase δh = 0.036 can be nulled by δΩm = -0.024 (δΩm h^2 ≈ -0.015), and A.4 shows that a proper CAMB+MCMC fit requires lower f_PBH and does not fully relieve the tension. Thus the 8.9% value is one point on a degeneracy, not a unique prediction. The abstract and Table 3 should be revised to present the MCMC results as the primary constraint, or to state the degeneracy explicitly.
  2. [§2.2.3–2.2.4] The paper assumes 100% deposition of Hawking luminosity into the recombining gas (§2.2.2), then in §2.2.3 notes that neutrinos carry away 40–50% of the total luminosity, and in §2.2.4 that tabulated deposition efficiencies exist but are not used. Since the heating rate enters linearly in the ionization boost factor (Eq. 2.15), this overestimates the effective heating by roughly a factor of two. Consequently, the f_PBH values quoted to achieve a given ΔH0/H0 are systematically underestimated. The calculation should be rerun with the standard deposition efficiency functions [33,57], or all abundance claims should be explicitly labeled as lower limits.
  3. [§2.4, Conclusions] The grey-body factor is described as ranging from 0.1% to unity and 'unknowable' to the extent that it depends on PBH spin and charge, but this uncertainty is not propagated into the results. The conclusions state that the PBH density should be multiplied by a grey-body factor without quantifying the resulting range. Because this factor can change the required abundance by orders of magnitude, the paper should present results as a function of the grey-body factor or give explicit ranges rather than quoting a single ΩPBH ≈ 10^-3 ΩC.
  4. [§3.1, Table 3, §A.4] The claim that PBH3 (ΩPBH ≈ 10^-3 ΩC, M^-1 IMF) is 'enough to entirely reduce' the Hubble tension is contradicted by the paper's own MCMC analysis in A.4, which shows that when the CMB power spectrum is actually fitted, lower f_PBH values are required and the tension is not fully relieved. The abstract and conclusions should be brought into line with the more cautious statement in §3.2 that PBHs could contribute to the tension but are unlikely to resolve it entirely.
minor comments (6)
  1. [§3.1] The sentence 'Simulation PBH7 (highest density of PBH)' appears to be an error; PBH8 has a higher f_C,PBH (10^-3 vs 10^-4), although the M^-2 IMF may produce stronger ionization.
  2. [Table 3 / Figure 4] The PBH3 row reports ΔH0/H0 > 8.9%, while Figure 4's caption says the red line is 8.7%. Please make these values consistent.
  3. [Eq. (2.11)] The exponent in the second term of α0 is unclear ('M_p^0'); please define M_p and ensure the formula is legible in the final version.
  4. [References] References [21] and [35] appear to refer to the same work (Mirpoorian, Jedamzik & Pogosian); please merge or clarify.
  5. [§2.3.2 / §3.1] The abrupt cutoff in heating and its effect on z* is acknowledged, but a quantitative estimate of the resulting systematic error would help the reader interpret Table 3, especially since the authors state z* values are lower limits.
  6. [Figure 1] The caption says 'The solid line is the degree of ionization, x_e' but the text refers to dashed lines as well; please clarify which curves correspond to Recfast and DarkHistory.

Circularity Check

0 steps flagged

No significant circularity: the forward PBH-recombination chain is self-contained; the main caveat is an acknowledged degeneracy (A.3/A.4), which weakens the headline but is not a circular reduction.

full rationale

The derivation chain is: Hawking mass-loss rate (Eq 2.10), energy conservation converted to ionisation boost factors (Eq 2.12-2.15), recfast integration of the modified ionisation history, z* from Eq 3.1, and Eq 3.3 converting Δz to ΔH0/H0. Each step uses external physics or the recfast code; the target H0 tension (8.7%) is not an input to the simulation. The later statement that ΩPBH ≈ 10^-4–10^-3 ΩC is 'required' is an inversion of the simulated ΔH0(f) relation against the known tension—an interpolation, not a hidden reuse of the target as a prediction. The same-author citation to Mould (2025) supplies the M^-1 IMF ansatz, but the paper explicitly tests an M^-2 IMF and presents the results as model-dependent, so the self-citation is not load-bearing. Section A.3 is a genuine limitation: the paper shows 'it is possible to null out an increase in h with a decrease in Ωm' (δh=0.036 nulled by δΩm=-0.024), so the 8.9% headline is not a unique CMB-inferred shift; A.4's MCMC fit finds lower f_PBH and the tension is 'not fully relieved.' This is a robustness/correctness caveat, not circularity. The abstract's 'entirely reduce' overstates the paper's own full analysis, but no load-bearing step reduces by definition to its inputs.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 0 invented entities

The headline f≈1e-3 is effectively a fit to the ~8.7% Hubble tension, modulated by an unconstrained grey-body factor that can range over orders of magnitude. The 100% deposition assumption and the abrupt M_max cutoff are acknowledged in the text but not folded into uncertainties. The Δz→ΔH0 mapping (Eq 3.3) is an approximation that the paper's own CAMB/MCMC fit undermines.

free parameters (6)
  • f_C,PBH (initial PBH fraction of dark matter) = 1e-3 in headline PBH3; range 1e-6–1e-2 explored
    Varied across simulations; the value 'required' to resolve the Hubble tension is found by inverting the simulated ΔH0-f relation to match the ~8.7% tension.
  • IMF power-law index α = -1 and -2
    Two shapes chosen by hand to represent different formation scenarios; affects ionization boost by factor 6.4.
  • M_max (maximum PBH mass) = 1e-18 or 1e-17.5 M_sun
    Chosen 'to maximise the impact on recombination' (§2.3.1); controls when heating truncates.
  • M_min (minimum PBH mass) = 1e-20 M_sun
    Lower bound of IMF; lighter PBHs evaporate before recombination.
  • Grey body factor ε = ~0.02 (from [63]); stated range 0.1%–100%
    Multiplier on Hawking spectrum; the paper says it is 'unknowable' to the extent it depends on spin/charge, introducing order-of-magnitude uncertainty.
  • Deposition efficiency = 1.0 (implicit)
    All electromagnetic Hawking energy is assumed deposited locally (§2.2.2); neutrinos carry away 40–50% (noted in §2.2.3), so this overestimates heating by ~2.
axioms (6)
  • standard math Hawking evaporation rate dM/dt = -(ℏc^4/G^2M^2) α0 (Eq 2.10)
    Imported from [36]; standard but not derived in this paper.
  • domain assumption All electromagnetic energy from PBH is deposited locally as heat/ionization: ΔE_gas = -ΔE_PBH (§2.2.2)
    Strong simplification; the authors note neutrino losses and redshift-dependent deposition as caveats but do not propagate them into the headline numbers.
  • domain assumption Ratio of baryons to dark matter is preserved in the environment of each PBH (Eq 2.5)
    Required to compute gas mass per PBH; if PBHs cluster or accrete differently, ΔT_gas and Δx change.
  • standard math Matter-dominated expansion at z* with 1+z ∝ t^-2/3, used to convert Δz to ΔH0 (Appendix A.2)
    Valid only for z in the matter-dominated regime and assuming fixed Ωm.
  • ad hoc to paper The CMB-inferred H0 responds to Δz by ΔH0/H0 = 3/2 Δz(1+z*)^-1 (Eq 3.3)
    This is the paper's own mapping; it ignores θ* degeneracies and is contradicted by the paper's MCMC fit.
  • domain assumption The mass window 10^-20–10^-17.5 M_sun is the relevant range for recombination-era evaporation
    Lighter PBHs are gone before recombination; heavier PBHs contribute negligibly; the choice 'maximises the impact' (§2.3.1).

pith-pipeline@v1.3.0-alltime-deepseek · 18306 in / 17318 out tokens · 186012 ms · 2026-08-01T15:08:41.599376+00:00 · methodology

0 comments
read the original abstract

Primordial black holes (PBHs) evaporate through Hawking radiation, emitting high-energy photons and ionising their surrounding environment. As contributors to the density of dark matter, Omega_C, if 10^-18 solar mass PBHs are present in the Universe they delay recombination and move the surface of last scattering of the cosmic microwave background (CMB). We perform recombination simulations using the software Recfast, and calculate the PBH fraction of dark matter required to resolve the Hubble tension. We find that nominally a cosmic PBH energy density of Omega_PBH ~ 10^-3 Omega_C would cause an 8.9% increase in the value of H_0, enough to entirely reduce the tension between the early- and late-time observations. This PBH fraction is modified by Gray Body Factors affecting Hawking radiation. Furthermore, also fitting the CMB leaves the Hubble tension not fully relieved with our present PBH prescription. Until relevant non-gravitational properties of the dominant dark matter species are ruled out, we suggest that the hypothesis that the ionisation history of the universe matches the thermal history of the standard LCDM cosmology is too precarious to hang the expansion rate on, and that it is better to measure H_0 locally at z <~ 1.

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