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Intrinsic Spectral Cosmology

A mix of human-written and AI-generated textHuman understanding: some partsmath-ph — Mathematical Physicsmath.AP — Analysis of PDEs

Contributed by Rajesh Dachiraju ↗

Version 1 / Oct 20, 2026 / CC BY 4.0

Abstract

We propose an intrinsic spectral cosmology based on intrinsic geometric wave mechanics, spectral dynamics, localized resonances, HJ source flow, and Hamilton--Jacobi gravity for point masses. The intrinsic field is represented through its time-local spectrum P(k,t)P(\mathbf k,t), whose second moment defines M2M_2, an intrinsic scale RI=M2−1/2R_I=M_2^{-1/2}, and HI=R˙I/RI=−M˙2/(2M2)H_I=\dot R_I/R_I=-\dot M_2/(2M_2). A canonical spectral Hamiltonian gives a conditional continuity equation and current Jk=∂h/∂(∇kθ)\mathbf J_k=\partial h/\partial(\nabla_k\theta); the actual Hamiltonian needed to determine that current is not fixed by the intrinsic space-time weak equation. We exhibit a minimal scale-drift Hamiltonian as a clearly labeled closure ansatz, not as a derived result. Gravity acts only between finite point masses through their Hamilton--Jacobi dynamics. Redshift, distance, structure formation, and the relation of localized resonances to masses remain hypotheses or open derivations. The framework makes no claim of empirical validation.

Provenance statement

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References

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Version history

  1. v1Submitted by Rajesh DachirajuInitial depositCurrentOct 20, 2026