Implications of a high growth index on the variation of $G$

TL;DR

The study addresses the tension between the observed high growth index $\gamma$ and the ΛCDM prediction by exploring time-varying Newton’s constant through two phenomenological $G_{ m eff}$ parametrizations. Using Cosmic Chronometers, DESI DR2 priors, and a Gaussian $\gamma$ likelihood, the authors demonstrate that a constant $G_{ m eff}$ is disfavored at up to $\sim3.4\sigma$, with evidence favoring $G_{ m eff}<G_N$ during the acceleration era. They find a roughly linear relation between $\gamma$ and the MG parameters, enabling simple forecasts and indicating that weaker gravity on cosmological scales can suppress structure growth. These results motivate Modified Gravity interpretations and highlight the potential of future surveys like Euclid to decisively test such scenarios.

Abstract

A recent determination of the growth index indicates a value significantly higher than the $Λ$CDM prediction, suggesting that alternative scenarios to $Λ$CDM may be required. In this work, we investigate whether a time-varying Newton's constant, $G_N$, can account for such a high growth index, $γ=0.063\pm0.025$. Adopting a phenomenological approach, we study two parameterizations of the effective gravitational coupling, $G_{\rm eff}$, one based on a Taylor expansion and another linked to the energy density parameter of Dark Energy. We constrain the models with Cosmic Chronometers (CC), Dark Energy Spectroscopic Instrument baryon acoustic oscillations (data release 2), CMB priors, and a gaussian likelihood for the growth index. We show that the constant $γ$ approximation is accurate for the parametrization linked to the energy density parameter of dark energy, but presents a non-negligible error for the other case, which we treat as a systematic error in the analysis. We find a $2.4σ-3.4σ$ tension level with constant $G_{\rm eff}$, depending on the parametrization. The results indicate that $G_{\rm eff}<G_N$ around the period of accelerated expansion, corresponding to a weaker effective gravitational interaction on cosmological scales, which leads to a suppression of the growth of cosmological structures.

Figures (4)

• Figure 1: Distribution of rms residuals for the constant growth index parameterization, with respect to $f$, considering different models of modified gravity under CC data. The distributions are normalized by the maximum value.
• Figure 2: Posteriors for the $g_{2}$ model with the measured value of the growth index considering residuals in the parametrization \ref{['eq:growth_rate-gamma']} ($\gamma=0.633\pm0.031$) together with either the cosmic chronometer (CC) dataset, in orange, or the DESI+CMB dataset, in blue.
• Figure 3: Posteriors for the $\mu_{0}$ model with the measured value of the growth index ($\gamma=0.633\pm0.025$) together with either the cosmic chronometer (CC) dataset, in orange, or the DESI+CMB dataset, in blue.
• Figure 4: Variation of $G_{\rm eff}$ for the two parametrizations considered as a function of redshift.