DCT-SBD-01 · DCT cluster

Stiffness–backreaction duality

A general bound on cosmological backreaction in solar-system-compatible Brans–Dicke theories

Nolan G. Parrott ORCID 0009-0009-8794-2589 Reserved DOI: 10.5281/zenodo.20032799 arXiv (primary): gr-qc

Download PDF LaTeX source (.tex) View on Zenodo

In one sentence: A short technical theorem: any Brans–Dicke theory that passes Cassini cannot use cosmological backreaction to explain dark energy at more than \(6 \times 10^{-10}\) of the observed value.

Read the paper

Your browser doesn't have a built-in PDF viewer. Download the DCT-SBD-01 PDF directly (0.25 MB).

Abstract

For any Brans–Dicke scalar–tensor theory satisfying the Cassini solar-system bound \(\omega_0\) > 40,000 on the dimensionless coupling, we prove that the contribution of cosmological backreaction to the effective dark-energy density is bounded above by \(6 \times 1\)0^{-10} \(\Lambda\) obs. The bound follows from a Jensen-type inequality on the Brans–Dicke stiffness (2\(\omega\) + 3)^{-1} averaged over Hubble-scale perturbations of the scalar field, combined with the standard Buchert averaging formalism extended to scalar–tensor cosmology. The result rules out backreaction-as-dark-energy explanations in any Brans–Dicke-class theory that respects solar-system constraints, independently of the specific form of the coupling function \(\omega\)(\(\phi\)) or the potential V(\(\phi\)). The duality is structural: the very stiffness that protects solar-system phenomenology mathematically forbids the scalar field from contributing meaningfully to large-scale acceleration through inhomogeneity-driven backreaction. We outline the application to Dimensional Coherence Theory and to general scalar–tensor extensions, including a comment on how the bound interacts with the disformal channel of theories that include both conformal and disformal couplings to matter. The result is a one-line theorem on a structurally simple class of theories; its proof requires only the Cassini bound, a convex Jensen inequality, and the linearised Buchert kinematic backreaction formula. We treat the result as a publishable side-result of the broader DCT cosmological program and present it standalone here so that it can be evaluated independently of any particular scalar–tensor model.

Keywords

Brans-Dickescalar-tensor gravitycosmological backreactionBuchert averagingCassini boundJensen's inequalitydark energyDimensional Coherence Theory

Cite

APA

Parrott, N. G. (2026). Stiffness–backreaction duality. Zenodo. https://doi.org/10.5281/zenodo.20032799

BibTeX 
@misc{parrott_dct_sbd_01_2026, author = {Parrott, Nolan G.}, title = {Stiffness–backreaction duality}, year = {2026}, publisher = {Zenodo}, doi = {10.5281/zenodo.20032799}, url = {https://doi.org/10.5281/zenodo.20032799}, note = {DCT-SBD-01, DCT paper cluster}
}
RIS 
TY - GEN
AU - Parrott, Nolan G.
PY - 2026
TI - Stiffness–backreaction duality
PB - Zenodo
DO - 10.5281/zenodo.20032799
UR - https://doi.org/10.5281/zenodo.20032799
ER -

This page is part of the public archive at dctheory.org. The PDF and .tex source above are byte-identical to the Zenodo deposit at 10.5281/zenodo.20032799.