{"paper":{"title":"A new duality relating density perturbations in expanding and contracting Friedmann cosmologies","license":"","headline":"","cross_cats":["astro-ph","gr-qc"],"primary_cat":"hep-th","authors_text":"Latham A. Boyle, Neil Turok, Paul J. Steinhardt","submitted_at":"2004-03-02T07:11:34Z","abstract_excerpt":"For a 4-dimensional spatially-flat Friedmann-Robertson-Walker universe with a scalar field $\\phi(x)$, potential $V(\\phi)$ and constant equation of state $w=p/\\rho$, we show that an expanding solution characterized by $\\epsilon=3(1+w)/2$ produces the same scalar perturbations as a contracting solution with $\\hat{\\epsilon}=1/\\epsilon$. The same symmetry applies to both the dominant and subdominant scalar perturbation modes. This result admits a simple physical interpretation and generalizes to $d$ spacetime dimensions if we define $\\epsilon \\equiv [(2d-5)+(d-1)w]/(d-2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0403026","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/0403026/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}