Modified Gravity from growth data: goodness-of-fit and gravitational coupling
Abstract
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 R2-corrected Appleby-Battye) using measurements of the growth rate f(z) and the matter fluctuation amplitude σ8(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, providing a physically motivated diagnostic that complements standard goodness-of-fit criteria. The Starobinsky and Hu-Sawicki models predict moderate departures from General Relativity, remaining compatible with constraints on both μ(z) and S8. In contrast, the R2-AB model predicts μ0 ∼ 3.5 and S8 = 0.638, a 3.2σ tension with Planck 2018, rendering it physically disfavored despite its competitive statistical performance.
Related
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BibTeX
@misc{filho2026modified,
title = {{Modified Gravity from growth data: goodness-of-fit and gravitational coupling}},
author = {Manoel V. S. Filho and Fernanda Oliveira and Wiliam S. Hipólito-Ricaldi and Felipe Avila and Armando Bernui},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21912},
eprint = {2609.21912},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21912},
}
RIS
TY - UNPB
TI - Modified Gravity from growth data: goodness-of-fit and gravitational coupling
AU - Manoel V. S. Filho
AU - Fernanda Oliveira
AU - Wiliam S. Hipólito-Ricaldi
AU - Felipe Avila
AU - Armando Bernui
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21912
UR - https://arxiv.org/abs/2609.21912
AB - 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, providing a physically motivated diagnostic that complements standard goodness-of-fit criteria. The Starobinsky and Hu-Sawicki models predict moderate departures from General Relativity, remaining compatible with constraints on both μ(z) and S_8. In contrast, the R^2-AB model predicts μ_0 ∼ 3.5 and S_8 = 0.638, a 3.2σ tension with Planck 2018, rendering it physically disfavored despite its competitive statistical performance.
ER -