Resolution of CMB Low-Multipole Anomalies and the Geometric Origin of Dark Matter Abundance Ratio (E_DM/E_Vis ≈ 5.42) in Prime-Prime Lattice Space

Standard ΛCDM cosmology encounters two fundamental challenges: the large-scale power deficit at low multipoles (l < 30) in the Cosmic Microwave Background (CMB) and the physical nature of the Dark Matter abundance ratio (Ωc/Ωb ≈ 5.47). Here, we present a unified geometric solution within the Prime-Prime Lattice (PPL) framework. Building upon the Legendre interval encapsulation and Z2 parity anomaly, PPL space defines the universe as a multiplicative phasor field governed by prime factorization scales. First, macro-scale spatial geometry is truncated by the primorial horizon boundary Λn = Pn# and screened by the infrared (IR) fixed point attractor C2 ≈ 0.660162, naturally suppressing the quadrupole (l = 2) power to ≈ 245 μK² and octupole (l = 3) power to ≈ 693 μK², matching Planck 2018 observations without fine-tuning. Second, on intermediate scales, Minimal-Step Prime Pair (MSPP) deficient quadratic cavities In = (n², (n+1)²) induce phase dissipation into the open vacuum |∅⟩ = 1. Numerical scanning reinforced by OEIS empirical verification up to n = 10⁷ (OEIS A091592) identifies the localized deficient set S_def = {1, 9, 19, 26, 27, 30, 34, 39, 49, 53, 77, 122}. We prove that the total multiplicative phase-dissipation factor M_DM = ∏_{n∈S_def} (1 + 1/n)² ≈ 8.51579 yields a strictly convergent physical dark matter energy E_DM = E0 ln M_DM ≈ 2.141931 E0 via logarithmic projection into physical energy space. Combined with visible base energy E_Vis = (ln(5/3))²/C2 ≈ 0.395271 E0, the resulting theoretical ratio E_DM/E_Vis ≈ 5.4189 agrees with Planck 2018 data within 0.92% error, proving that Dark Matter is the geometric residual of primordial phase dissipation.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-19
DOI
https://doi.org/10.5281/zenodo.22839807
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

Resolution of CMB Low-Multipole Anomalies and the Geometric Origin of Dark Matter Abundance Ratio (E_DM/E_Vis ≈ 5.42) in Prime-Prime Lattice Space

Shuichi Wada
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

Resolution of CMB Low-Multipole Anomalies and the Geometric Origin of Dark Matter Abundance Ratio (E_DM/E_Vis ≈ 5.42) in Prime-Prime Lattice Space

Shuichi Wada
preprint en

Abstract

Standard ΛCDM cosmology encounters two fundamental challenges: the large-scale power deficit at low multipoles (l < 30) in the Cosmic Microwave Background (CMB) and the physical nature of the Dark Matter abundance ratio (Ωc/Ωb ≈ 5.47). Here, we present a unified geometric solution within the Prime-Prime Lattice (PPL) framework. Building upon the Legendre interval encapsulation and Z2 parity anomaly, PPL space defines the universe as a multiplicative phasor field governed by prime factorization scales. First, macro-scale spatial geometry is truncated by the primorial horizon boundary Λn = Pn# and screened by the infrared (IR) fixed point attractor C2 ≈ 0.660162, naturally suppressing the quadrupole (l = 2) power to ≈ 245 μK² and octupole (l = 3) power to ≈ 693 μK², matching Planck 2018 observations without fine-tuning. Second, on intermediate scales, Minimal-Step Prime Pair (MSPP) deficient quadratic cavities In = (n², (n+1)²) induce phase dissipation into the open vacuum |∅⟩ = 1. Numerical scanning reinforced by OEIS empirical verification up to n = 10⁷ (OEIS A091592) identifies the localized deficient set S_def = {1, 9, 19, 26, 27, 30, 34, 39, 49, 53, 77, 122}. We prove that the total multiplicative phase-dissipation factor M_DM = ∏_{n∈S_def} (1 + 1/n)² ≈ 8.51579 yields a strictly convergent physical dark matter energy E_DM = E0 ln M_DM ≈ 2.141931 E0 via logarithmic projection into physical energy space. Combined with visible base energy E_Vis = (ln(5/3))²/C2 ≈ 0.395271 E0, the resulting theoretical ratio E_DM/E_Vis ≈ 5.4189 agrees with Planck 2018 data within 0.92% error, proving that Dark Matter is the geometric residual of primordial phase dissipation.

Zenodo (CERN European Organization for Nuclear Research)
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Resolution of CMB Low-Multipole Anomalies and the Geometric Origin of Dark Matter Abundance Ratio (E_DM/E_Vis ≈ 5.42) in Prime-Prime Lattice Space — Shuichi Wada · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS