{"paper":{"title":"Threshold of primordial black hole formation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-ph","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Chul-Moon Yoo, Kazunori Kohri, Tomohiro Harada","submitted_at":"2013-09-17T07:03:30Z","abstract_excerpt":"Based on a physical argument, we derive a new analytic formula for the amplitude of density perturbation at the threshold of primordial black hole formation in the universe dominated by a perfect fluid with the equation of state $p=w\\rho c^{2}$ for $w\\ge 0$. The formula gives $\\delta^{\\rm UH}_{H c}=\\sin^{2}[\\pi \\sqrt{w}/(1+3w)]$ and $\\tilde{\\delta}_{c}=[3(1+w)/(5+3w)]\\sin^{2}[\\pi\\sqrt{w}/(1+3w)]$, where $\\delta^{\\rm UH}_{H c}$ and $\\tilde{\\delta}_{c}$ are the amplitude of the density perturbation at the horizon crossing time in the uniform Hubble slice and the amplitude measure used in numeric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4201","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}