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. These models predict a negative spectral running ($\alpha_s<0$), 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 $\alpha_s$, 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 $\alpha_s$ and the running of the running $\beta_s$. For most dataset combinations, moving from $\Lambda$CDM to EDE increases the inferred $\alpha_s$: once the acoustic angular scale $\theta_s$ is fixed, EDE increases the diffusion-to-acoustic angular scale ratio $\theta_d/\theta_s$, and the shift in $\alpha_s$ 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 $\alpha_s$ may be premature, especially until the Hubble tension, and more generally the pre-recombination expansion history, is understood.