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CETOmega: The Causal-Informational Completion of Gravity

Christian Balfagon

Abstract

We present CETOmega, a unified framework that completes gravity through a causal-informational principle. The theory reconciles general relativity and quantum mechanics within a strictly four-dimensional, nonlocal, and causal formulation. At its core lies an analytic and retarded kernel K^-1(Box_R), derived from a discrete causal network, which governs the propagation of the gravitational and scalar sectors. A scalar field, the texon, emerges as the effective excitation of causal connectivity and accounts simultaneously for dark matter and dark energy without introducing extra degrees of freedom or breaking locality. The formalism ensures analyticity, spectral positivity, and holographic completeness. The kernel admits a Stieltjes representation with positive spectral density rho(mu) greater than or equal to zero, guaranteeing unitarity and causal propagation. At cosmological scales, CETOmega predicts stable inflationary dynamics consistent with Planck observations. Black hole ringdown frequencies acquire perturbative corrections controlled by the causal scale and remain subleading for astrophysical black holes within the fiducial window l* between 10^-5 and 10^-4 meters, where l* defines the mean causal correlation length of the texonic field. CETOmega thus provides a complete, causal, and informational foundation for spacetime dynamics, recovering Einstein gravity in the infrared while extending its validity to the quantum and cosmological domains.

CETOmega: The Causal-Informational Completion of Gravity

Abstract

We present CETOmega, a unified framework that completes gravity through a causal-informational principle. The theory reconciles general relativity and quantum mechanics within a strictly four-dimensional, nonlocal, and causal formulation. At its core lies an analytic and retarded kernel K^-1(Box_R), derived from a discrete causal network, which governs the propagation of the gravitational and scalar sectors. A scalar field, the texon, emerges as the effective excitation of causal connectivity and accounts simultaneously for dark matter and dark energy without introducing extra degrees of freedom or breaking locality. The formalism ensures analyticity, spectral positivity, and holographic completeness. The kernel admits a Stieltjes representation with positive spectral density rho(mu) greater than or equal to zero, guaranteeing unitarity and causal propagation. At cosmological scales, CETOmega predicts stable inflationary dynamics consistent with Planck observations. Black hole ringdown frequencies acquire perturbative corrections controlled by the causal scale and remain subleading for astrophysical black holes within the fiducial window l* between 10^-5 and 10^-4 meters, where l* defines the mean causal correlation length of the texonic field. CETOmega thus provides a complete, causal, and informational foundation for spacetime dynamics, recovering Einstein gravity in the infrared while extending its validity to the quantum and cosmological domains.
Paper Structure (31 sections, 31 equations, 4 figures, 3 tables)

This paper contains 31 sections, 31 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Action principle
  4. Equations of motion
  5. Causality and well-posedness
  6. Consistency conditions
  7. Cosmology and Predictions
  8. Effective Friedmann equations
  9. Inflationary regime
  10. Late-time acceleration and dark sector
  11. Observable predictions
  12. Black Hole Phenomenology
  13. Causal regularization and effective geometry
  14. Quasi-normal modes and observational window
  15. Thermodynamics and the Causal Second Law
  16. ...and 16 more sections

Figures (4)

  • Figure 1: Predicted CMB power spectrum of CET$\Omega$ (blue solid) compared with the Planck 2018 data (gray points) and $\Lambda$CDM baseline (dashed). CET$\Omega$ remains within $1\sigma$ over the entire multipole range, with a mild suppression at high $\ell$ due to causal smoothing.
  • Figure 2: Schematic scaling of the perturbative QNM suppression $\bigl|\delta\omega/\omega\bigr|\sim(\ell_*/r_H)^2$ for the fundamental mode ($\ell=2,n=0$) as a function of the causal scale $M_*^{-1}$. Within the fiducial parameter window, the effect remains subleading for astrophysical black holes. Implications for detectability are discussed in the context of future detectors bambi2013regularlisa2017mission.
  • Figure 3: CMB temperature power spectrum in CET$\Omega$ for representative values of $M_*$ compared with $\Lambda$CDM. Residuals remain below $10^{-4}$ across the full multipole range.
  • Figure 4: Schematic representation of the Causal–Informational Triangle (TCI). Each vertex—geometry, causality and information— mutually determines the others. CET$\Omega$ achieves their closure under the Principle of Minimal Causality (PCM).