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Preprint . 2026
License: CC BY
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image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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The Geometric Quadrupole: Metric Stiffening and the Calibration of Cosmic Structure

Authors: Woodward, Vance;

The Geometric Quadrupole: Metric Stiffening and the Calibration of Cosmic Structure

Abstract

Precision cosmology faces a persistent tension between the high structure growth (S8) predicted by Planck CMB data and the lower S8 measured by local weak lensing surveys like KiDS and DES. Standard models interpret this as a failure of structure growth over time. This paper proposes that the S8 tension is instead a spatial calibration error resulting from the use of Newtonian gravity on a scale-dependent scalar manifold. We identify a mechanism called the Geometric Quadrupole, where the scalar metric stiffens at cluster scales, effectively amplifying the gravitational field by approximately 18 percent relative to the Newtonian prediction. By correcting for this metric stiffening, we demonstrate that the locally observed S8 value aligns perfectly with the Planck prediction, resolving the tension without invoking Dark Energy or modifying the temporal history of the universe.

Keywords

S8 Tension, Weak Lensing, Callibration Error, Toroidal Scale Dynamics, Geometric Quadrupole, Metric Stiffening, Sigma8, Hubble Tension, Structure Growth, Cosmology

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green