{
  "id": "oai:papers.qnfo.org:ultrametric-p-adic-vacuum-energy-suppression-and-the-cosmological-constant",
  "slug": "ultrametric-p-adic-vacuum-energy-suppression-and-the-cosmological-constant",
  "title": "Ultrametric p‑adic Vacuum Energy Suppression and the Cosmological Constant",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The observed dark‑energy density ρ_Λ^rm obs≈10^-47 GeV⁴ is smaller than the naïve quantum‑field‑theoretic vacuum estimate by roughly 10¹20, a discrepancy that dominates the cosmological‑constant problem. Existing proposals retain the Archimedean real number field as the sole arena for physics, leaving the non‑Archimedean completions of Q unused. This work fills the gap by (i) explicitly evaluating the adelic product ∏_v|q|_v=1 for rational test modes q=2 and q=6, (ii) deriving the p‑adic zero‑point energy for a free scalar on a Bethe‑lattice and showing that the naïve p‑adic contribution is larger than the real one, (iii) computing the matching condition ω₀=(p-1)Λ⁴/(16π²) for p=3, which yields a suppression factor 1.27×10^-2 relative to Λ⁴, and (iv) analysing the residual vacuum energy after adelic cancellation. The real‑sector vacuum density with a Planck cutoff Λ_rm Pl=1.22×10¹9 GeV is ρ_rm vac^rm real=1.40×10⁷4 GeV⁴, while the p=3 adelic contribution is ω₀=2.81×10⁷4 GeV⁴. The adelic product eliminates the quartic divergence but leaves a countable sum whose magnitude is not fixed by the product formula; an additional regularisation (e.g. subtraction of a constant term) would be required to reach ρ_Λ^rm obs. If these analytic results hold, the cosmological‑constant hierarchy can be reduced by a topological identity rather than by anthropic or dynamical fine‑tuning, offering a concrete pathway for theoretical cosmologists to incorporate ultrametric structures into quantum‑gravity models.",
  "abstract_markdown": "The observed dark‑energy density $\\rho_{\\Lambda}^{\\rm obs}\\approx10^{-47}\\,\\text{GeV}^4$ is smaller than the naïve quantum‑field‑theoretic vacuum estimate by roughly $10^{120}$, a discrepancy that dominates the cosmological‑constant problem. Existing proposals retain the Archimedean real number field as the sole arena for physics, leaving the non‑Archimedean completions of $\\mathbb{Q}$ unused. This work fills the gap by (i) explicitly evaluating the adelic product $\\prod_{v}|q|_{v}=1$ for rational test modes $q=2$ and $q=6$, (ii) deriving the $p$‑adic zero‑point energy for a free scalar on a Bethe‑lattice and showing that the naïve $p$‑adic contribution is larger than the real one, (iii) computing the matching condition $\\omega_{0}=(p-1)\\Lambda^{4}/(16\\pi^{2})$ for $p=3$, which yields a suppression factor $1.27\\times10^{-2}$ relative to $\\Lambda^{4}$, and (iv) analysing the residual vacuum energy after adelic cancellation. The real‑sector vacuum density with a Planck cutoff $\\Lambda_{\\rm Pl}=1.22\\times10^{19}\\,\\text{GeV}$ is $\\rho_{\\rm vac}^{\\rm real}=1.40\\times10^{74}\\,\\text{GeV}^4$, while the $p=3$ adelic contribution is $\\omega_{0}=2.81\\times10^{74}\\,\\text{GeV}^4$. The adelic product eliminates the quartic divergence but leaves a countable sum whose magnitude is not fixed by the product formula; an additional regularisation (e.g. subtraction of a constant term) would be required to reach $\\rho_{\\Lambda}^{\\rm obs}$. If these analytic results hold, the cosmological‑constant hierarchy can be reduced by a topological identity rather than by anthropic or dynamical fine‑tuning, offering a concrete pathway for theoretical cosmologists to incorporate ultrametric structures into quantum‑gravity models.",
  "date": "2026-10-20",
  "first_published": "2026-10-20",
  "last_revised": "2026-10-20T00:00:00Z",
  "modified": "2026-10-20T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/ultrametric-p-adic-vacuum-energy-suppression-and-the-cosmological-constant",
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  "version_url": "https://papers.qnfo.org/papers/ultrametric-p-adic-vacuum-energy-suppression-and-the-cosmological-constant/v/1.0.0",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "Ultrametric p‑adic Vacuum Energy Suppression and the Cosmological Constant"
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    "publicationYear": "2026",
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        "description": "The observed dark‑energy density ρ_Λ^rm obs≈10^-47 GeV⁴ is smaller than the naïve quantum‑field‑theoretic vacuum estimate by roughly 10¹20, a discrepancy that dominates the cosmological‑constant problem. Existing proposals retain the Archimedean real number field as the sole arena for physics, leaving the non‑Archimedean completions of Q unused. This work fills the gap by (i) explicitly evaluating the adelic product ∏_v|q|_v=1 for rational test modes q=2 and q=6, (ii) deriving the p‑adic zero‑point energy for a free scalar on a Bethe‑lattice and showing that the naïve p‑adic contribution is larger than the real one, (iii) computing the matching condition ω₀=(p-1)Λ⁴/(16π²) for p=3, which yields a suppression factor 1.27×10^-2 relative to Λ⁴, and (iv) analysing the residual vacuum energy after adelic cancellation. The real‑sector vacuum density with a Planck cutoff Λ_rm Pl=1.22×10¹9 GeV is ρ_rm vac^rm real=1.40×10⁷4 GeV⁴, while the p=3 adelic contribution is ω₀=2.81×10⁷4 GeV⁴. The adelic product eliminates the quartic divergence but leaves a countable sum whose magnitude is not fixed by the product formula; an additional regularisation (e.g. subtraction of a constant term) would be required to reach ρ_Λ^rm obs. If these analytic results hold, the cosmological‑constant hierarchy can be reduced by a topological identity rather than by anthropic or dynamical fine‑tuning, offering a concrete pathway for theoretical cosmologists to incorporate ultrametric structures into quantum‑gravity models.",
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