{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"3c4190e5cb1bcdcafee3ffb8afca1a0ac118ec1a2e1d46646978e5267d77fc9c","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","f44ba42244dca05fdd5d5da6bcee7a4c193df894b212d210bfd6fb6363f77b8a"],"salt":"fc0b675ff8467ae503c66eb41a994c0f01704c958b794d7d64209b7b636919e0","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cosmo.primordial-black-holes.small-scale-power","kind":"well-posed","literature_status":"open","n":"2","parents":[],"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.","posed_since":"","precise":"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 $k$.","problem_ref":"f44ba42244dca05fdd5d5da6bcee7a4c193df894b212d210bfd6fb6363f77b8a","references":"","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.","status_note":"","title":"Is the primordial curvature spectrum enhanced on small scales?","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"90590671c8d2474b7acd568edbdd9a964aa69cc4bea0920ed608337ba8b2c7a4","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"27e02fcbcbf1cec9ccfd2cf0b8b0c42ae0b51bac840db5e6eafea3d3f2ddeb4c","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"xW6wZ4yxlngag2o6iycH_wqLBoT9mrdBVS20YFe18LrLoMIvsAboh-PV_u3irpGVEY-D1dzESF5awxVcCNCuCA"},"schema":"pubphys.envelope/1"},"record_hash":"90590671c8d2474b7acd568edbdd9a964aa69cc4bea0920ed608337ba8b2c7a4","leaf_index":3160}