{"schema":"pubphys.bundle/1","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},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"90590671c8d2474b7acd568edbdd9a964aa69cc4bea0920ed608337ba8b2c7a4","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"27e02fcbcbf1cec9ccfd2cf0b8b0c42ae0b51bac840db5e6eafea3d3f2ddeb4c","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"xW6wZ4yxlngag2o6iycH_wqLBoT9mrdBVS20YFe18LrLoMIvsAboh-PV_u3irpGVEY-D1dzESF5awxVcCNCuCA"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIJ-Avy8vxzsnM_SzwuLDEKuC1G6yEDbXm6v6j0_Ld60zwICgS0cpUVZsUGDQ8tekLBT2P5YsZGZeuMEaooWQdp8wNCPEgdji0yOZ3aiQ2DrwALN9gNZo6B9rEzFjtjzUYBQOYVLgI8CCEESwCTgDGX4NJu7qPHl1UD8M3SweHPvh6-lLkoi0HGwjxIPJ9wwaAvLWVgpeMZVbCc6flyEbC5ihd8AXJIWxRbiRYCPEgiPzga-LZrx9byCWzhBjxMYNQ5ee6hiBeRGpT_vha760I8CD0D46W4-C3YA-DQVOUCzUlv3mKZXw-ulRAbN1T6M92xAjwIFL42owBJVURGnb4sFPQtSoKAW3ToV9h6LojAsi6KdcQCPAg_wIiPkLJd3-DTpBID5KVkTGoJ2F0twCyomKLdpQPO3UI8CDsCcIzBovmyR1v7IXhYg1Z7m0X4dWZvLS_NU94HSk3sQjxIJdQdDsL3v2lA7qZb8kMJtOgaTQmbgchdPcS5lYJqDLnCPAgkPXX-naXR0fRIdS-sEDlzYmtMvSCNH42ESUF0QXb6NUI8CDQo_sIWZiWXaTGRSQBLmU-lHJKskYKqsjO1r02DhB8LAj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIvIG30nGjXVeju3iD3D6Q4buGOzpOKyT8v6Ae-521AeTwILykpYtHExGuoO2fubVgcTvnX7MJ9NkfLDZz4Gm7H6aRCPEg1SeuWigqTChjkkvHynRNi05T-Qy17_4Ds_6DGgoA29EI8CB8VlQCWQlbvEmVwcijF3GVR_Im0BoJm6-HUBycS5nfkwjxIBw-laaFJV3WTf04LgMc_mHgYcZzQKqHcYX1abKIXSHjCPEgvJQAzDL2agLUZcyg3I-Bnvv-NCq3sZgprba61EylttwI8CA4nJ8ltAzLfcK2q2BIZKAS5JW2dkOGfc10zbAD3n0c-AjwIIg82Jvk6sG9d_qFEsDPR33QWZO6pmDRJWIBF6p7sCc5CPEgraRI2npokG3tsYuZYconfMt0ARYLxAQQuCOiQUqeUM8I8SDArwsGYVuomKH_DJiJGziPwECn7skqn20TGM58Ezco0wjwIIgwugvlgSNOmTWMhquqetKjeLf0x7d1a1MH4KU52JbFCPAg3mczMYDKOd7Nhf3ojA9ZvuTsN66Y1NnyYTp9j8GKQNwI8SCvAiiN-Hrv7IEejd8wdUihoozu5KOvpoBFJ0vg3UnGAQj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"]},"log":{"leaf_index":"3160","tree_size":"3804","proof":["ef20e66638095c7d50acb85a1c7a4707bd64e588ccc430a6f6a5eb4e11fb774f","701c921bd418e9471c253e38a4ec89abac1e98a674d9b6ec96e2e6c2cd869711","b202a3f3ae47e74ed3deff360d3ea9e15c9cad21caad7685cf5d4cb72266f6c0","6f7d4880e721eb1e76566ae6ad4e2670a6651fbfd34aa84153952fe521dc277e","b9d72c5ccec7ded6c6447e21ad2644afda068bcf89da50e3e454abd999cf726c","281c3457265e9f609db70810d62e17cfa504355f1f22415898df8325ea7599b5","d7aa9bcc125a881b729a20bf9875af594205e69ea0a81ae6ee0ccef9a0ef2f44","5426917e21a76a04dade5c5485f552ff526bc237fdd43d7b4658d73e661cc956","48906313613fdfddd2bd907650210a7f3e59ccb380a2b862e892089f41bcdced","98b5a14b42b3a202b6ef825f66833fa505601404c4c0f14575f3ec922607a858","af34d80d0065c0ab502282775e865492e2cb49c9493f4594d63ba5577922854a","3c578dccc15502c5f3efe228cadc99fee76ab536ed01f66b14d316fdcc157429"],"checkpoint":"pubphys.com/log/v1\n3804\nAK6t4qgu96+M9wScTrIlsJ10d/zhKVEtYguyM3aeJvo=\n\n— pubphys.com/log/v1 JFPwIPP8EtoxgcsQg7V7CwIdL4UKPqJtpv+eB8sFNJjyQHIdyA1VabmBsPyLqq2bLxJPn57rA6fQi8y0QDDjRXHvlQg=\n","promise":"pubphys.com/log/v1 promise\nb1373ce22133932a20237b97fd71b26744658c1ab22a773ac461f54a0cda120d\n3160\n2026-10-15T23:43:57Z\n2026-10-16T01:43:57Z\n\n— pubphys.com/log/v1 JFPwINs1CqKt0MyOqn47kLYMWPLvMsme93UNnp0Fi2JxY2aKkuJtpMkIbJQxUeSB6EJ+Td5LVA6v8wNYo4hnfNR1ogU=\n"},"orcid_key_evidence":[],"attesting":null}