The Variational Efficiency Framework: Pre-Registration of Cosmological Observables for LIGO Run 5 and Euclid DR1

Overview

The Variational Efficiency Framework (VEF) provides a radical, mathematically closed departure from standard $\Lambda$CDM cosmology, positing that the universe operates as a static, closed, action-conservative geometric manifold. Rather than kinematic expansion, cosmic redshift is derived as an intrinsic efficiency degradation $(\eta_{eff})$ of the propagating wave packet, driven by the geometric folding of the manifold.

This thesis provides a unified geometric and thermodynamic theory that reproduces major observational benchmarks—including galactic rotation curves and the Hubble tension—without invoking dark matter, dark energy, or inflation.

Key Scientific Contributions

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  Resolution of the Hubble Tension: Derives the $3/2$ Coordination Law and "Structural Debt" ($D_{struct} \approx 0.146$) to reconcile early and late-universe Hubble measurements ($67.4$ vs. $73.2 \text{ km/s/Mpc}$).

   

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  Emergent Gravity: Formulates gravity as a thermodynamic phenomenon arising from the dissipation of action variance governed by the Replicator Master Equation.

   

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  The Litim Efficiency Floor: Utilizes the Wetterich Functional Renormalization Group and Litim regulators to establish a UV cutoff of $\approx 2.17 \times 10^{-18} \text{ s}^{-1}$, resolving zero-efficiency singularities.

   

Immediate Testable Predictions (Pre-Registration)

This document serves as a formal pre-registration of specific, falsifiable predictions for the 2026 observational window:

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   Gravitational-Wave Damping: Predicts a strain amplitude attenuation of exactly $\eta_{eff}(z) = 1/(1+z)$ for all binary black hole mergers.

    

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   LIGO Run 5: Predicts $\approx 16.7\%$ attenuation for events at $z \approx 0.2$ and $\approx 33.3\%$ for $z \approx 0.5$.

    

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   Euclid DR1 (October 2026): Predicts a measured cosmic-web binding-energy fraction of $14.6 \pm 0.5\%$ of critical density.

    

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   Black Hole Phenomenology: Predicts the absence of long-lived echoes due to the momentum-space nature of the Litim regulator.

    

Methodology & Validation

The framework is supported by a numerical validation suite (MATLAB) demonstrating Global Asymptotic Stability via LaSalle's Invariance Principle. Validation against the Unified Galaxy HI Rotation Curve Corpus (Flynn 2026) confirms the bimodal distribution of the scale-dependent Poincaré constant