Are single-field models of inflation and PBHs production ruled out by ACT observations?

The data release from the Atacama Cosmology Telescope (ACT) imposes stronger constraints on primordial black holes (PBHs) formation in single-field inflation models versus the Planck data. In particular, the updated Cosmic Microwave Background (CMB) radiation measurements favour a {\it higher} scalar spectral index $n_s$ and its {\it positive} running $α_s$, which put the single-field models under scrutiny. Even in the absence of PBHs production, the new data constrain many single-field models of inflation. To explore this tension, we study PBHs formation in a concrete viable $α$-attractor E-model. We investigate an impact of bending of the inflaton potential plateau toward reconciling the model with the ACT bounds on the CMB observables. We find that attempts to increase $n_s$ through bending lead to negative values of $α_s$. Those values are disfavored by the ACT bounds just above $2σ$ even for PBHs in the asteroid-mass range, while the tension becomes stronger for heavier PBHs.