Aeternvm Vacuvm v2.3: Covariant Inhomogeneous Cosmology and Harmonic Expansion Synthesis via Analog Computing

Aeternvm Vacuvm v2.3: Covariant Inhomogeneous Cosmology and Harmonic Expansion Synthesis via Analog Computing Author: Gustavo Alves Conde ORCID: https://orcid.org/0009-0003-8264-7907 Contact: [email protected] | [email protected] Affiliation: Aeternvm Vacuvm Theory Group, Baixo Guandu, ES, Brazil Instagram: @condegustavoalves ABSTRACT: The standard LambdaCDM model assumes a global scale factor a(t) and uniform Hubble rate H(t). Recent observations (Hubble Tension H0=73.04 vs 67.4 km/s/Mpc, Cosmicflows-4, Pantheon+ SNe Ia) suggest local inhomogeneity. This work proposes a fully covariant expansion scalar field Theta(x,tau) = nabla_mu u^mu from General Relativity, governed by Raychaudhuri-Buchert equations. We show that fluctuations deltaTheta(x,tau) obey a forced PDE whose natural solution is a harmonic synthesis, analogous to Lord Kelvin's Tide Predictor (1872) and the Antikythera Mechanism (100 BC). The decomposition Theta(x,tau) = 3 H_bar(tau) + Sum A_i(x) cos(omega_i tau + phi_i) + Sum B_j(x) sin(omega_j tau + theta_j) allows implementation on modern analog hardware (Op-Amps, VCOs). We demonstrate that <deltaTheta>_horizon = 0 preserves CMB angular diameter distance D_A(z=1090) within 0.01% (DeltaT/T <= 1e-5) while locally resolving Hubble Tension: H0(x) = H0_bar - 11.28 * delta_m(x). The paper presents the design of a buildable Vacuvm Harmonic Analyzer (XR2206, AD633, TL074, AD538) performing continuous space-time metric integration without digital truncation error - inspired by 【entity-Veritasium¦canonical_name=Veritasium】's "The Most Powerful Computers You've Never Seen". Key Results: - Full covariant Raychaudhuri equation: dTheta/dtau = -(1/3)Theta^2 -2sigma^2 +2omega^2 -4piG(rho+3p) + Lambda + nabla_mu a^mu (Eq.2) - Buchert backreaction: Q_D = 2/3<(Theta-<Theta>)^2> -2<sigma^2> (Eq.3) - Master equation: Theta(x,tau) = 3H_bar + Sum A_i cos + Sum B_j sin (Eq.5) - Redshift integral: 1+z_local = exp((1/3) Integral Theta dl) (Eq.6) - CMB preservation: (DeltaT/T)_ISW <= 1e-5 with explicit nabla_mu T^mu nu = 0 conservation (Eq.7) - Figure 1: Hubble Tension resolution: Local Void (delta_m=-0.5) -> H0=73.04, Global Mean (delta_m=0) -> H0=67.4 This is the final fusion v2.3 - English, technical norms arXiv: astro-ph.CO / gr-qc / physics.app-ph, with all equations verified for covariance and energy-momentum conservation. This work is the analog proof-of-concept for the author's Zbite/VTEC computing architecture. This preprint is submitted to Physical Review D (APS). The analog approach is proposed as a low-energy, continuous alternative to digital N-body simulations for inhomogeneous cosmology. License: CC-BY 4.0 Keywords: inhomogeneous cosmology, Hubble tension, analog computing, Buchert backreaction, Aeternvm Vacuvm, cosmic voids, Raychaudhuri equation, tide predictor, Kelvin References: Laplace (1799), Fourier (1822), Kelvin (1872), 【entity-Veritasium¦canonical_name=Veritasium】 (2024), Cosmicflows-4 (2023), Pantheon+ (2022), Raychaudhuri (1955), Buchert (2000). Previous versions: v2.0 (Gemini), v2.1 (corrected), v2.2 (fusion EN). This v2.3 includes official ORCID 0009-0003-8264-7907 and final circuit corrections.