Modified Gravity from growth data: goodness-of-fit and gravitational coupling — E8 Intelligence Research

While background expansion data alone cannot discriminate among cosmological models, the growth of large-scale structures directly probes the underlying theory of gravity, offering a path to distinguish General Relativity from its modifications. In this work, we constrain three representative $F(R)$ modified gravity models (Starobinsky, Hu-Sawicki, and $R^2$-corrected Appleby-Battye) using measurements of the growth rate $f(z)$ and the matter fluctuation amplitude $σ_8(z)$. Our analyses combine MCMC parameter estimation, Gaussian Process reconstructions, and goodness-of-fit statistics including Akaike information criterion (AIC) and Bayesian information criterion (BIC). All investigated models provide statistically comparable fits to the current growth data, with information criteria differences too small to establish a preference for any particular scenario. To overcome this degeneracy, we reconstruct the effective gravitational coupling $μ(z)$ from the MCMC posterior samples, providi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com