{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"5f1ce28215a5c994b6497dcdf75b0ba30e10f014502d660b3fb7aa9a23b2a424","created":"2026-10-03T07:18:02Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"36727685cb1158bf3825dc388bdb29d128797786e86ccb5bc4f2d2cbe9342317","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":"1","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 $P_{\\zeta} \\sim 2.1e-9$ 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 $k$.","problem_ref":null,"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":"9ab792b7e278762046677161a5c3d97a4c12042fe341bebc00b0f937c2c50d7a"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"f44ba42244dca05fdd5d5da6bcee7a4c193df894b212d210bfd6fb6363f77b8a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"7232f2ea9f5b6e40e2e3bf3d37f632ba67b7fdc926f18eb32bdc4a62cd739937","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"zQJHQbZIR1KKw9Bc0aipsfhpLvmHAOSZ84W1ha5VyuNAIcXSb_DaiNyI4QZzlZnNcHh_Dt6IXhA8XDReiCvHBw"},"schema":"pubphys.envelope/1"},"record_hash":"f44ba42244dca05fdd5d5da6bcee7a4c193df894b212d210bfd6fb6363f77b8a","leaf_index":1273}