Beware of the running $n_s$ when producing heavy primordial black holes

TL;DR

This paper investigates how recent ACT observations of positive spectral index running constrain single-field inflation models for primordial black hole formation, highlighting challenges for producing massive PBHs while remaining consistent with CMB data.

Contribution

It demonstrates the impact of observed spectral index running on ultra-slow-roll inflation models and introduces a Markov Chain Monte Carlo method to explore model parameter spaces.

Findings

Positive running constrains large PBH formation in USR models.

Asteroid-mass PBHs remain feasible dark matter candidates.

Non-minimally coupled polynomial inflation favors inflection points for CMB consistency.

Abstract

We examine single-field inflationary models for the formation of primordial black holes (PBHs). By analyzing the latest observations from the Atacama Cosmology Telescope (ACT)~\cite{ACT:2025fju, ACT:2025tim}, we demonstrate that the observed preference for positive running ($\alpha_s$) of the scalar spectral index $n_s$ imposes significant restrictions on the parameter space for a large class of ultra-slow-roll (USR) models. This tension becomes progressively pronounced for more massive PBHs, posing substantial challenges for USR models to yield a detectable PBH abundance, especially in the mass range probed by ongoing and future gravitational-wave experiments such as LIGO-Virgo-KAGRA and the Einstein Telescope. However, this discrepancy is minimal for asteroid-mass PBHs, which are still capable of feasibly constituting the entirety of dark matter. To numerically probe the six-dimensional parameter space of the models, we adapted a Markov Chain Monte Carlo approach to efficiently scan over the viable configurations. Our results further indicate that, in non-minimally coupled polynomial inflation, a viable cosmic microwave background (CMB) spectrum is best obtained at an inflection point for which second-order slow-roll approximation is necessary for precise CMB predictions.