Running into tension: primordial black holes from ultra-slow-roll inflation, spectral running, and the Hubble tension
Single-field ultra-slow-roll (USR) inflation is among the most studied mechanisms for primordial black hole (PBH) formation. When a non-stationary inflection point close to CMB scales is present, these models predict a negative spectral running ($α_s<0$), whose magnitude increases with the PBH mass. This is in tension with recent hints for positive running from Atacama Cosmology Telescope (ACT) Cosmic Microwave Background (CMB) data. However, inflationary parameters inferred from CMB data are sensitive to the assumed pre-recombination expansion history, which is precisely where new physics motivated by the Hubble tension should operate. Focusing on axion-like early dark energy (EDE) as a benchmark, we investigate the effect of such pre-recombination new physics on $α_s$, and hence on the viability of USR PBH models, in light of state-of-the-art CMB data from Planck, ACT, and the South Pole Telescope, together with Baryon Acoustic Oscillation data from DESI DR2. Our analysis therefore provides an updated set of constraints on $α_s$ and the running of the running $β_s$. For most dataset combinations, moving from $Λ$CDM to EDE increases the inferred $α_s$: once the acoustic angular scale $θ_s$ is fixed, EDE increases the diffusion-to-acoustic angular scale ratio $θ_d/θ_s$, and the shift in $α_s$ compensates this extra damping by increasing small-scale power. In this sense, tension calls for tension: taking the Hubble tension seriously as an indication for new physics strengthens the challenges faced by USR PBH models. More broadly, our analysis stresses that inflationary model selection using CMB-inferred inflationary parameters such as $n_s$ and $α_s$ may be premature, especially until the Hubble tension, and more generally the pre-recombination expansion history, is understood.