What question did this study set out to answer?

This work aims to develop a comprehensive framework for the spectral evolution of layered expansion in cosmology.

June 29, 2026Open Access

R-layer Mode Theory (RLMT) XLVIII: Spectral Evolution Equation for Layered Expansion (Complete Edition with Appendices A–K)

Key Points

This work aims to develop a comprehensive framework for the spectral evolution of layered expansion in cosmology.
Derivation of the time-dependent spectral evolution equation for Hubble eigenmodes.
Analysis of nonlinear Rayleigh corrections and introduction of higher-order Hubble eigenvalues.
Construction of a predictive framework for future cosmological surveys.
Developed a complete dynamical and nonlinear formulation for layered expansion.
Unified the theory with the AUP/MUP/CUP particle-physics hierarchy.
Established a complete operator-theoretic foundation for layered expansion cosmology.

Abstract

This volume develops the full dynamical, nonlinear, and particle‑physics‑unified formulation of the layered expansion.We derive the time‑dependent spectral evolution equation for the Hubble eigenmodes, analyze nonlinear Rayleigh corrections, introduce higher‑order Hubble eigenvalues, and construct a predictive framework for future cosmological surveys.The theory naturally unifies with the AUP/MUP/CUP particle‑physics hierarchy and provides a complete operator‑theoretic foundation for layered expansion cosmology.

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