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The Auxetic Vacuum: A Geometric-Mechanical Resolution to the Dark Sector and Cosmological Tensions

Authors: Rall;

The Auxetic Vacuum: A Geometric-Mechanical Resolution to the Dark Sector and Cosmological Tensions

Abstract

This essay proposes a foundational resolution to the dark sector and Hubble tension by defining the physical vacuum not as a passive geometric background, but as an auxetic Cosserat (micropolar) solid governed by electroweak symmetry breaking. By modeling the vacuum's Poisson's ratio purely as a function of the weak mixing angle ($\nu_{vac} = -\tan^2\theta_W \approx -0.301$), we eliminate the need for ad-hoc dark parameters. Our geometric framework accurately derives the cosmic mass ratio ($\Omega_c/\Omega_b \approx 5.40$), predicts a phantom dark energy equation of state ($w \approx -1.03$), and fully resolves the Hubble tension by translating early-universe longitudinal measurements into late-universe transverse observables via an exact dimensional anisotropy factor.

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