Running Under Tension: Primordial Black Holes, Spectral Running, and the Hubble Tension ✛ ✎ ✦
Context
Primordial black holes (PBHs) are one of the most intriguing candidates for the role of dark matter. They could have formed from overdense clumps in the early universe, which arise from a sharp enhancement of primordial curvature perturbations during inflation. One popular mechanism for such enhancement is an ultra-slow-roll (USR) phase in single-field inflation, first proposed by Alan Guth. However, data on the cosmic microwave background, particularly from the ACT telescope, point to a positive spectral running $α_s$, while USR models predict $α_s$ < 0. This conflict calls into question the very idea of PBH formation this way. Adding to the intrigue is the Hubble tension—a discrepancy in measurements of the Hubble constant, which may indicate unknown physics in the epoch before recombination. The authors investigate how such new physics (exemplified by early dark energy) affects $α_s$ and, consequently, this debate.
Methods
To study the influence of pre-recombination physics on $α_s$, the scientists used the Monte Carlo Markov Chain (MCMC) method and Bayesian analysis. They generated 32 model variants, combining data on the cosmic microwave background from three experiments—Planck, ACT, and SPT—along with baryon acoustic oscillation (BAO) data from the DESI DR2 instrument. The baseline models were ΛCDM and an extension with axion-like early dark energy (EDE), where the Friedmann equations are solved together with the Klein–Gordon equation. In some models, the running of the running of the spectral index, $β_s$, was also varied.
Results
The main result: for most data combinations, the transition from ΛCDM to EDE increases the central value of $α_s$. For example, when combining all three cosmic microwave background experiments (CMB-SPA) within ΛCDM, $α_s$ = 0.0054±0.0050, while in EDE $α_s$ = 0.0063±0.0057. Adding DESI data hardly changes the picture. This shift, though small (~0.1–0.5σ), is systematic. The physical reason is that EDE, in order to resolve the Hubble tension, reduces the sound horizon by ~7%, which forces an increase in the ratio of the diffusion angular scale to the acoustic scale ($θ_d$/$θ_s$). To compensate for the additional damping in the tail of the cosmic microwave background spectrum, more power is required on small scales, which is achieved by increasing $α_s$ (as well as $n_s$). Importantly, this effect directly follows from Hubble's law and the Friedmann equations, linking the expansion of the universe to angular scales. When the authors translated the $α_s$ constraints onto the PBH mass plane, it turned out that using the most complete dataset (CMB-SPA+DESI) in the EDE model, even the asteroid-mass window (~$10^{-17}$–$10^{-12}$ M_⊙) is closed at the 2σ level. In other words, accounting for the Hubble tension does not rescue USR models; rather, it amplifies their conflict with observations. Interestingly, the sensitivity to the choice of CMB experiment is very high: data from ACT alone exclude almost the entire range of PBH masses, while SPT currently lacks sufficient precision.
Implications
These results underscore a crucial methodological lesson: the inflationary parameters ($n_s$ and $α_s$) extracted from cosmic microwave background data are not direct measurements of the power spectrum of primordial inflationary perturbations. They depend on the assumed cosmological model, in particular on the physics before recombination. As long as the nature of the Hubble tension remains unclear, any selection of inflation models based on such parameters is premature. The work also shows that if the Hubble tension is real and requires new physics, then USR inflation as a mechanism for producing PBHs faces even greater difficulties. In particular, solar and sub-solar PBHs, important for gravitational wave detectors, are under even greater pressure from the data.
Future development
In the future, data from new cosmic microwave background experiments, such as the Simons Observatory and CMB-S4, will significantly refine constraints on $α_s$ and test the robustness of the conclusions. It is also important to study other early dark energy models and more general pre-recombination physics scenarios to understand how universal the discovered effect is. Developing non-inflationary mechanisms for generating PBHs or exploring multi-field inflation models may point the way to resolving the tensions.
Impact
The results directly impact the cosmology of the early universe, inflationary models, and black hole physics, as well as the interpretation of data from gravitational-wave detectors LIGO, Virgo, KAGRA, and future observatories such as the Einstein Telescope and LISA, which search for mergers of PBHs.
Next steps
It is necessary to repeat the analysis for other early dark energy models (e.g., new EDE, AdS EDE) and to study how the choice of a specific USR inflation implementation affects the relationship between α_s and PBH mass. It is also important to improve the consistency of data from different CMB experiments to rule out instrumental systematics.
Key open problems
The article directly addresses several open problems in modern physics: the Hubble tension, the nature of dark matter (if PBHs are a component), the problem of initial conditions for inflation, and the question of how to correctly extract information about the physics of the early universe from cosmological observations.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The study investigates the influence of early dark energy (EDE) on the spectral run α_s in the context of primordial black hole (PBH) formation. The authors performed a Bayesian analysis using data from Planck, ACT, SPT, and DESI, combining them in 32 model variants. They show that EDE systematically increases the central value of α_s by ~0.1–0.5σ, which could alleviate the tension with ultraslow-roll (USR) models predicting a negative run.
Where its strength is
A key strength is the systematic analysis of how pre-recombination physics affects the crucial parameter α_s, which links the Hubble tension and PBH formation. This paves the way for reconciling observational constraints with theoretical models.
Where it could go next
- It might be interesting to see how alternative PBH production mechanisms that do not require a USR phase are consistent with a positive α_s. In our archive, there is a nearby paper on PBH production from magnetic fields, where the perturbation spectrum may have a different shape.based on: The Cosmic Magnetic Bow: How Primordial Black Holes Are Born arXiv:2606.23307
- It would be curious to test how modified expansion in the early universe (similar to EDE) affects the collapse efficiency and PBH mass function. The archive contains an analysis considering slow reheating after inflation, which changes the collapse dynamics.based on: Cosmic sous-vide: How slow reheating resurrects primordial black holes arXiv:2605.11332v2
- It is interesting to compare the obtained constraints on α_s with predictions from models where PBHs affect the expansion rate of the universe. In one of the neighboring papers, it is investigated how PBH evaporation can change the expansion rate, which is indirectly related to the Hubble tension.based on: Cosmic Hot Tap: How Primordial Black Holes Rewrite the Speed of the Universe arXiv:2607.18528v1
Worth trying
- Check whether the increase in α_s persists when using alternative parameterizations of EDE (e.g., with a different potential).
- Calculate the PBH mass function for the obtained α_s ranges and compare with microlensing constraints.
- Investigate the combined effect of EDE and nonzero β_s on inflationary parameter constraints.
Why this may matter
The work connects two major problems in modern cosmology—the nature of dark matter and the Hubble tension—through the common parameter α_s. If the positive run is confirmed, it would indicate the need to revise standard PBH formation scenarios and might open new avenues for testing early dark energy.
Nearby works in our archive
- Black Holes Instead of Dark Energysimilarity 0.65
- How the Birth of the Universe Controls Dark Energy Todaysimilarity 0.65
- Tiny Black Holes Don’t Warp the Cosmossimilarity 0.65
- The Cosmic Magnetic Bow: How Primordial Black Holes Are Bornsimilarity 0.64
- How Tiny Black Holes Are Born from a Slowed-Down Expansionsimilarity 0.64
- Cosmic Hot Tap: How Primordial Black Holes Rewrite the Speed of the Universesimilarity 0.64
- Cosmic sous-vide: How slow reheating resurrects primordial black holessimilarity 0.63
The closest work in the archive sits at 0.65 by meaning — the usual level for our corpus.
A asteroid-mass primordial black hole (~$10^{-16}$ M_⊙) would have a radius smaller than a proton, yet could weigh as much as a mountain. If such objects make up dark matter, several of these microscopic black holes pass through each of us every year without causing harm.
The idea of primordial black holes as dark matter is explored in science fiction: for example, in Peter Watts' novel 'Blindsight,' such objects are used to explain gravitational anomalies.
Key numbers
- α_s (CMB-SPA, ΛCDM): 0.0054 ± 0.0050
- α_s (CMB-SPA, EDE): 0.0063 ± 0.0057
- Reduction of sound horizon r_drag: ~7%
- Enhancement of power spectrum from CMB to PBH scales: from ~10⁻⁹ to ~10⁻²
- Characteristic PBH masses from USR inflation: from ~10⁻¹⁷ M⊙ to ~10² M⊙