A new study examines single-field inflation models capable of generating large curvature perturbations at sub-Mpc scales without conflicting with cosmological observations. The work pinpoints a central tension: amplifying primordial perturbations at very small scales clashes with the scalar spectral index nₛ measured by the ACT and SPT telescopes, a result that rules out several conventional single-field inflation models.

To circumvent this obstacle, the authors propose three viable classes of inflationary potentials: bump/dip-modified potentials, step-like potentials, and potentials with a double inflection point. Each of these families sufficiently amplifies primordial perturbations while predicting nₛ values that fall within the 2σ range of current observational bounds.

The analysis examines the primordial power spectra predicted by these models and constrains their parameter spaces by combining cosmological observations across different scales: the cosmic microwave background (CMB), baryon acoustic oscillations (BAO), primordial black hole (PBH) abundance, pulsar timing arrays (PTA), and CMB distortions. The results show that some of the models considered can simultaneously satisfy the ACT/SPT constraints and account for current PTA observations, although doing so while respecting the constraints on primordial black hole abundance remains challenging.

The question remains open: reconciling the PTA signal with strict PBH limits will require further refining these potentials or exploring additional variants. The study highlights how precision CMB measurements at large angular scales and observations at sub-Mpc scales complement each other to constrain the physics of the very early universe.