A phenomenological power-law suppression of small-scale power: observational status, and why the published radion Lagrangian cannot produce it

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-18
DOI
https://doi.org/10.5281/zenodo.20607635
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

A phenomenological power-law suppression of small-scale power: observational status, and why the published radion Lagrangian cannot produce it

Andre Swart Andre
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

A phenomenological power-law suppression of small-scale power: observational status, and why the published radion Lagrangian cannot produce it

Andre Swart Andre
preprint en

Abstract

A phenomenological power-law suppression of small-scale power: observational status, and why the published radion Lagrangian cannot produce it Version 2.0.0 Resource type Preprint Publication date 2026-09 (September 2026) Authors Swart, Andre — GeometricCosmo (Independent Researcher), Cape Town, South Africa Full description STATUS: Negative result. Supersedes the observational claims of versions 1.8.x and 1.9.x of this project, which should not be cited for the conclusions listed in the errata (Appendix D of the attached paper). SUMMARY Version 1.9.1 reported that a broken power-law transfer function, T(k) = 1 for k < 1.5 h/Mpc and T(k) = (1.5/k)^0.5 above it, simultaneously passed S_8 and Lyman-alpha constraints while leaving sigma_8 too high, and attributed this curve to a radion in a 5D Gauss-Bonnet braneworld coupled to the electromagnetic sector. This release freezes that function and its reported numbers as an immutable control, then tests both the curve and the attribution independently. Neither survives. WHAT INDEPENDENT VERIFICATION FOUND 1. The transfer function does not move sigma_8. An independent CAMB 2.0.4 run at fixed A_s (no amplitude rescaling) shows a fractional change of -4.8e-5, because only 0.048% of the sigma_8 variance lies above the break scale k_c = 1.5 h/Mpc. A function equal to 1 below k_c cannot alter sigma_8 regardless of its behaviour above that scale. 2. S_8 and sigma_8 are the same measurement. With Omega_m fixed, S_8 = 1.02501 * sigma_8 identically, so the reported pattern of an S_8 pass alongside a sigma_8 failure cannot occur. The corrected values are sigma_8 = 0.8112 and S_8 = 0.8315, both 1.7-sigma above their (mutually consistent) targets. 3. The reported Lyman-alpha ratio of 0.891 used a non-standard convention (P_mod = T*P rather than the standard P_mod = T^2*P) and averaged in two sampling points at which T is identically 1 by construction. Under the standard convention, suppression reaches 70% at k = 5 h/Mpc and is excluded. 4. Reducing the published radion equation of motion in the quasi-static limit gives an effective gravitational coupling G_eff(k,a)/G = 1 + 2*beta^2 * k^2/(k^2 + a^2*m_eff^2). This fails in three independent ways: the correction is proportional to beta^2 and therefore always positive (the mechanism enhances clustering rather than suppressing it); the k-dependence is a saturating Yukawa step rather than a declining power law; and because the coupling reaches non-relativistic matter only through electromagnetic binding energy, the strength needed for a percent-level effect is excluded by Cassini and MICROSCOPE by at least four, and plausibly many more, orders of magnitude. 5. A previously reported screening factor of 10^42 is withdrawn as a category error. It measured the ratio of background source strengths, not a screening factor. The corrected statement is stronger: the Lagrangian contains no screening mechanism (chameleon, symmetron or Vainshtein) at all. WHAT IS NOT AFFECTED The 5D background numerics (warp factor solved to residual < 6e-6) and the CAMB pipeline / reproducibility infrastructure are sound and unchanged. The failure is in the observational analysis and in the attribution of the fitted curve to the Lagrangian, not in the numerical machinery. WHAT THIS MEANS FOR THE PROPOSED 6D EXTENSION A move to 6D codimension two flux compactification, intended to derive the break scale k_c from geometry, is deferred. None of the failures above depends on the number of extra dimensions: the derived G_eff follows from any light scalar with a healthy kinetic term coupled linearly to matter through F^2, in five, six, or any other number of dimensions. The single useful next calculation is an explicit dimensional reduction of the 5D action, sufficient to determine whether the induced matter coupling is conformal (as assumed here) or of a derivative/disformal type that could evade the sign argument. CONTENTS OF THIS UPLOAD - radion_leakage_v2.0.pdf Full paper (16 pp.): derivation, corrected observational baseline, three independent failure modes, requirements for a successor mechanism, and a full errata list against versions 1.8.x-1.9.x. - paper.tex LaTeX source. - V2.0_BASELINE_LOCKED.md Frozen Layer-1 definitions (transfer function, cosmology, observable definitions) as an immutable control for future work. - verify_baseline.py Independent CAMB run and observable extraction. Reproduces every number in the paper in under two minutes. - make_figures.py Regenerates all five figures from the verification output. - baseline_verification.json Numerical output of the verification run. - pk_baseline.csv Linear P(k), T(k), and the sigma_8 integrand. - figures/ fig1_window.png, fig2_s8_sigma8.png, fig3_lyman_alpha.png, fig4_geff.png, fig5_coupling.png. REPRODUCE pip install camb numpy scipy matplotlib python verify_baseline.py python make_figures.py RELATION TO PRIOR VERSIONS v1.8.2 Exponential T(k) superseded v1.8.3 sigma_8 = 0.76 from the stated T(k) incorrect, not reproducible v1.9.0 S_8/Lyman-alpha mutually exclusive directionally correct v1.9.1 Power-law T(k) passes S_8 and Lyman-alpha RETRACTED (this release) v2.0 Baseline fails; mechanism falsified current The v1.9.0 conclusion was closer to correct than the v1.9.1 revision that replaced it. The reversal traces to the two convention errors identified in this release. Keywords cosmology modified gravity braneworld Gauss-Bonnet radion S8 tension sigma8 Lyman-alpha forest equivalence principle scalar-tensor gravity Damour-Donoghue coupling falsification negative result reproducibility Subjects (Zenodo controlled vocabulary / arXiv-style) Physics :: Cosmology and Nongalactic Astrophysics (astro-ph.CO) Physics :: General Relativity and Quantum Cosmology (gr-qc) License Documents / paper text : CC BY 4.0 Code (verify_baseline.py, make_figures.py) : MIT Data (baseline_verification.json, pk_baseline.csv) : CC0 (Zenodo takes one license per deposit; CC BY 4.0 is the right single choice if forced to pick one, since the paper text is the primary object and the code is short enough to be reasonably covered by it. Note the MIT/CC0 split for the individual files in the description field, as above.) Related / alternate identifiers Is new version of 10.5281/zenodo.21663023 (v1.9.1 retracted by this release) Is supplemented by https://github.com/GeometricCosmo/gb-leakage-cmb (Software) The "Is new version of" relation is filled in automatically if you use the New version button from the v1.9.1 record rather than starting a fresh deposit check that it's still present before publishing. Notes field (Zenodo has a separate "Notes" box use it for this) This version retracts the S8/Lyman-alpha resolution claim and the sigma_8 "constraint" framing of v1.9.1. See the errata (Appendix D of the attached PDF) for the specific statements that should no longer be cited.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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