Is the primordial curvature spectrum enhanced on small scales?

The curvature power spectrum is $P_{\zeta} \sim 2.1 \times 10^{-9}$ at $k = 0.05\,\mathrm{Mpc}^{-1}$, while a cosmologically relevant PBH abundance needs $P_{\zeta} \sim 10^{-2}$ at the scale entering the horizon at formation. Measure or bound $P_{\zeta}(k)$ for $k > 1\,\mathrm{Mpc}^{-1}$ using CMB spectral distortions (the COBE/FIRAS mu-distortion limit is about three orders of magnitude stronger than the PBH limit at $k \sim 10^{1} \text{ to } 10^{4}\,\mathrm{Mpc}^{-1}$, Chluba, Erickcek and Ben-Dayan 2012), scalar-induced gravitational waves in pulsar-timing, LISA and ground-based bands, and ultracompact minihalos. An answer is a detected enhancement or an upper bound below the PBH-forming level at each $k$.

A PIXIE-class spectral-distortion measurement plus scalar-induced gravitational-wave searches by pulsar timing arrays and LISA covering the PBH-relevant k range.