{
  "abstract": "We identify the initial velocity v0 in the exact solution of Non-Equilibrium Dynamics\n\n(NED) as the contraction velocity near R = 2ℓp, and we propose the concrete value\n\nv0 = −2.5 × 10130 m/s .\n\nThis identification implies that the universe was contracting in the past. Using the exact\n\nsolution\n\n2R\n\n3 − 3ℓpR\n\n2 = 3Kt2 + 12ℓ\n\n2\n\np\n\nv0 t + 4ℓ\n\n3\n\np\n\n,\n\nwe derive the time at which the expansion velocity vanishes,\n\ntR˙ =0 = −\n\n2ℓ\n\n2\n\np\n\nv0\n\nK\n\n≈ 9.7 × 109\n\nyears,\n\nthe corresponding radius,\n\nRR˙ =0 ≈ 1.69 × 1026 m,\n\nand the time required for the universe to return to R = 2ℓp,\n\nt\n\nfuture\n\nbounce = −\n\n4ℓ\n\n2\n\np\n\nv0\n\nK\n\n≈ 1.94 × 1010 years.\n\nWe also compute the cosmic age with v0 included:\n\ntnow =\n\n−2ℓ\n\n2\n\np\n\nv0 +\n\n√\n\n4ℓ\n\n4\n\np\n\nv\n\n2\n\n0 −\n\nKc\n\n3\n\nK\n\n,\n\nwhere c = 4ℓ\n\n3\n\np − 2R3\n\nnow + 3ℓpR2\n\nnow. For v0 = −2.5 × 10130 m/s, we obtain\n\ntnow ≈ 2.14 × 1010 years ,\n\nwhich is closer to the observed value 1.38 × 1010 years than the v0 = 0 result 6.4 × 109\n\nyears. With constant v0, the equation admits only two times at which R = 2ℓp: t = 0\n\nand t = −4ℓ\n\n2\n\np\n\nv0/K. This means that the universe undergoes at most two bounces and does\n\nnot repeat periodically. However, if v0 (or F0) varies in time, the universe can undergo\n\nrepeated expansion–contraction cycles. Since the speed of light does not limit the expansion\n\nor contraction of space in NED, the large value of v0 is not physically excluded.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "takashi ueda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2zmpknyfh4gb8.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23474906",
  "fulltext_url": null,
  "id": "2zmpknyfh4gb8",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23474906",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23474906/files/%E8%86%A8%E5%BC%B5%E3%81%A8%E5%8F%8E%E7%B8%AE%20(1).pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2zmpknyfh4gb8.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:06Z",
      "native_id": "23474906",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23474906"
    }
  ],
  "subjects": [],
  "title": "Cyclic Cosmic Expansion in Non-Equilibrium Dynamics: Identification of the Initial Velocity v0 as the Contraction Velocity near R = 2ℓp, Past Contraction, Future Turning Points, Cosmic Age, and Repeated Cycles",
  "title_text": "Cyclic Cosmic Expansion in Non-Equilibrium Dynamics: Identification of the Initial Velocity v0 as the Contraction Velocity near R = 2ℓp, Past Contraction, Future Turning Points, Cosmic Age, and Repeated Cycles",
  "type": "preprint",
  "updated_at": "2026-11-02T12:21:06Z",
  "url": "https://research.draconitic.com/paper/2zmpknyfh4gb8",
  "venue": "Zenodo",
  "versions": []
}