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  "slug": "efimov-like-log-periodic-modulations-in-the-cosmic-microwave-background-power-sp",
  "title": "Efimov‑Like Log‑Periodic Modulations in the Cosmic Microwave Background Power Spectrum: Theory and Prospects for Detection",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The temperature anisotropy power spectrum of the Cosmic Microwave Background (CMB) is a cornerstone of precision cosmology, yet subtle signatures of discrete scale invariance (DSI) have not been systematically explored. A specific DSI scenario, inspired by the Efimov effect, predicts a log‑periodic modulation of the form Acos bigl(2πln ℓ/ln q+φbigr) with scaling factor q=e or π superimposed on the standard ΛCDM angular power spectrum C_ℓ. Preliminary Lomb‑Scargle analysis of the 83‑bin Planck 2018 TT spectrum yields a non‑detection with p-values in the interval 0.65–0.91; the short effective baseline of roughly four oscillation cycles limits statistical power. This paper formalizes the theoretical amplitude expected from generic DSI mechanisms, derives the number of observable cycles for the full unbinned Planck spectrum (ℓ≈2–2500), and quantifies the improvement in detection significance achievable with a matched‑filter analysis that incorporates the full Planck covariance matrix. Assuming a modest modulation amplitude of A=10^-3 (0.1 % of the primordial spectrum) the projected signal‑to‑noise ratio reaches 3.2σ, sufficient for a decisive test. The result would either open a new observational window on early‑universe physics or place stringent upper bounds on DSI‑driven processes.",
  "abstract_markdown": "The temperature anisotropy power spectrum of the Cosmic Microwave Background (CMB) is a cornerstone of precision cosmology, yet subtle signatures of discrete scale invariance (DSI) have not been systematically explored. A specific DSI scenario, inspired by the Efimov effect, predicts a log‑periodic modulation of the form  \n\\(A\\cos\\!\\bigl(2\\pi\\ln \\ell/\\ln q+\\phi\\bigr)\\)  \nwith scaling factor \\(q=e\\) or \\(\\pi\\) superimposed on the standard \\(\\Lambda\\)CDM angular power spectrum \\(C_\\ell\\). Preliminary Lomb‑Scargle analysis of the 83‑bin Planck 2018 TT spectrum yields a non‑detection with \\(p\\)-values in the interval \\(0.65\\)–\\(0.91\\); the short effective baseline of roughly four oscillation cycles limits statistical power. This paper formalizes the theoretical amplitude expected from generic DSI mechanisms, derives the number of observable cycles for the full unbinned Planck spectrum (\\(\\ell\\approx2\\)–\\(2500\\)), and quantifies the improvement in detection significance achievable with a matched‑filter analysis that incorporates the full Planck covariance matrix. Assuming a modest modulation amplitude of \\(A=10^{-3}\\) (0.1 % of the primordial spectrum) the projected signal‑to‑noise ratio reaches \\(3.2\\sigma\\), sufficient for a decisive test. The result would either open a new observational window on early‑universe physics or place stringent upper bounds on DSI‑driven processes.",
  "date": "2026-10-20",
  "first_published": "2026-10-20",
  "last_revised": "2026-10-20T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/efimov-like-log-periodic-modulations-in-the-cosmic-microwave-background-power-sp",
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    "titles": [
      {
        "title": "Efimov‑Like Log‑Periodic Modulations in the Cosmic Microwave Background Power Spectrum: Theory and Prospects for Detection"
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