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Title: Is the primordial curvature spectrum enhanced on small scales?
Plain: The microwave background shows that early density ripples had a strength of about one part in 20,000 on large scales. Forming black holes needs ripples thousands of times stronger on much smaller scales, which some inflation models predict.
Precise: The curvature power spectrum is $P_{\zeta} \sim 2.1e-9$ at $k = 0.05\,\mathrm{Mpc}^{-1}$, while a cosmologically relevant PBH abundance needs $P_{\zeta} \sim 1e-2$ 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 $k \sim 1e1 \text{ to } 1e4\,\mathrm{Mpc}^{-1}$, 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 $k$.
Settled by: A PIXIE-class spectral-distortion measurement plus scalar-induced gravitational-wave searches by pulsar timing arrays and LISA covering the PBH-relevant k range.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: (empty)
Posed since: (empty)