{"paper":{"title":"Solutions of the wave equation bounded at the Big Bang","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"gr-qc","authors_text":"Jorge Drumond Silva, Jos\\'e Nat\\'ario, Pedro M. Gir\\~ao","submitted_at":"2018-09-25T18:00:11Z","abstract_excerpt":"By solving a singular initial value problem, we prove the existence of solutions of the wave equation $\\Box_g\\phi=0$ which are bounded at the Big Bang in the Friedmann-Lemaitre-Robertson-Walker cosmological models. More precisely, we show that given any function $A \\in H^3(\\Sigma)$ (where $\\Sigma=\\mathbb{R}^n, \\mathbb{S}^n$ or $\\mathbb{H}^n$ models the spatial hypersurfaces) there exists a unique solution $\\phi$ of the wave equation converging to $A$ in $H^1(\\Sigma)$ at the Big Bang, and whose time derivative is suitably controlled in $L^2(\\Sigma)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09633","kind":"arxiv","version":3},"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"}