A Planck 2018 Test of Relational Gravity via the Dark Energy Equation of State — A Controlled w_0CDM Comparison with LCDM

This paper presents a controlled cosmological test of the Relational Gravity (RG) framework using Planck 2018 cosmic microwave background data. We perform a direct comparison between a baseline w_0CDM control run and an RG-motivated extension in which the dark energy equation-of-state parameter w_0 is allowed to vary, while all other cosmological parameters, priors, likelihoods, and numerical settings are held fixed. Using CLASS and Cobaya, Markov Chain Monte Carlo analyses are carried out on Planck 2018 temperature-only likelihoods. The results indicate a statistically significant shift toward a quintessence-like equation of state (w_0 > -1) at the \sim 1.5\sigma level, while leaving standard cosmological parameters statistically unchanged. The numerical artefacts required to reproduce the results — including configuration files, raw MCMC chains, analysis notebooks, and derived figures — are publicly available via a companion Zenodo record: Reproduction Kit DOI: https://doi.org/10.5281/zenodo.17969495 This record contains the paper PDF only and should be cited independently from the reproduction materials.