{"paper":{"title":"Exponential potentials and cosmological scaling solutions","license":"","headline":"","cross_cats":["astro-ph","hep-ph"],"primary_cat":"gr-qc","authors_text":"Andrew R Liddle, David Wands, Edmund J Copeland","submitted_at":"1997-11-21T16:13:48Z","abstract_excerpt":"We present a phase-plane analysis of cosmologies containing a barotropic fluid with equation of state $p_\\gamma = (\\gamma-1) \\rho_\\gamma$, plus a scalar field $\\phi$ with an exponential potential $V \\propto \\exp(-\\lambda \\kappa \\phi)$ where $\\kappa^2 = 8\\pi G$. In addition to the well-known inflationary solutions for $\\lambda^2 < 2$, there exist scaling solutions when $\\lambda^2 > 3\\gamma$ in which the scalar field energy density tracks that of the barotropic fluid (which for example might be radiation or dust). We show that the scaling solutions are the unique late-time attractors whenever th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9711068","kind":"arxiv","version":2},"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"}