χ‑Spectral Geometry of Cosmological Mass Renormalization: Operator‑Topological Reconstruction of the Perimeter Institute "Dark Force" Effect
Abstract
Recent cosmological analyses, including those addressing the tension between Dark Energy Spectroscopic Instrument (DESI) observational constraints and cosmic microwave background (CMB) measurements, led to the Perimeter Institute “dark force” paradox: introducing an attractive self‑interaction among dark matter constituents enhances local clumping efficiency while simultaneously inducing an effective decay of particle mass as the Universe expands, thereby suppressing global large‑scale structure growth. This paper establishes the first operator‑topological reconstruction of this phenomenon within the χ‑spectral geometry of the Zero‑Entropy Background Topological Structure (ZEBTS‑SUPER). In this framework, mass is not an intrinsic, irreducible substance property, but an operator‑spectral modulus generated by the non‑commutative interaction between the background self‑adjoint operator D and the boundary projection operator P_chi. We prove that cosmological expansion acts as an operator modular flow on the spectrum of the boundary derivation B = [D, P_chi], naturally driving a spectral renormalization of mass m_eff(t) = m_0 * exp(‑integral(gamma_chi(t') dt')). The anomalous “lightening” observed in dark‑force simulations is rigorously demonstrated to be a pure geometric artifact of spectral curvature flow and Tomita‑Takesaki modular evolution across the χ‑boundary. This operator reconstruction completely resolves the DESI‑CMB cosmological tension without appealing to physical dark matter particles or ad hoc dark energy fields.
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BibTeX
@misc{mukha2026χspectral,
title = {{χ‑Spectral Geometry of Cosmological Mass Renormalization: Operator‑Topological Reconstruction of the Perimeter Institute "Dark Force" Effect}},
author = {Anatolii Mukha},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = aug,
doi = {10.5281/zenodo.21826132},
url = {https://doi.org/10.5281/zenodo.21826132},
note = {CC BY},
}
RIS
TY - UNPB
TI - χ‑Spectral Geometry of Cosmological Mass Renormalization: Operator‑Topological Reconstruction of the Perimeter Institute "Dark Force" Effect
AU - Anatolii Mukha
PY - 2026
DA - 2026/08/06
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.21826132
UR - https://doi.org/10.5281/zenodo.21826132
AB - Recent cosmological analyses, including those addressing the tension between Dark Energy Spectroscopic Instrument (DESI) observational constraints and cosmic microwave background (CMB) measurements, led to the Perimeter Institute “dark force” paradox: introducing an attractive self‑interaction among dark matter constituents enhances local clumping efficiency while simultaneously inducing an effective decay of particle mass as the Universe expands, thereby suppressing global large‑scale structure growth. This paper establishes the first operator‑topological reconstruction of this phenomenon within the χ‑spectral geometry of the Zero‑Entropy Background Topological Structure (ZEBTS‑SUPER). In this framework, mass is not an intrinsic, irreducible substance property, but an operator‑spectral modulus generated by the non‑commutative interaction between the background self‑adjoint operator D and the boundary projection operator P_chi. We prove that cosmological expansion acts as an operator modular flow on the spectrum of the boundary derivation B = [D, P_chi], naturally driving a spectral renormalization of mass m_eff(t) = m_0 * exp(‑integral(gamma_chi(t') dt')). The anomalous “lightening” observed in dark‑force simulations is rigorously demonstrated to be a pure geometric artifact of spectral curvature flow and Tomita‑Takesaki modular evolution across the χ‑boundary. This operator reconstruction completely resolves the DESI‑CMB cosmological tension without appealing to physical dark matter particles or ad hoc dark energy fields.
ER -