A recent determination of the growth index indicates a value significantly higher than the $\mathrm{\Lambda }$ cold dark matter (CDM) prediction, suggesting that alternative scenarios to $\mathrm{\Lambda }\mathrm{CDM}$ 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, $\gamma =0.633_{-0.025}^{+0.024}$. Adopting a phenomenological approach, we study two parametrizations of the effective gravitational coupling, $G_{\mathrm{eff}}$, one based on a Taylor expansion and another linked to the energy density parameter of dark energy. We constrain the models with cosmic chronometers, Dark Energy Spectroscopic Instrument baryon acoustic oscillations (Data Release 2), cosmic microwave background priors, and a Gaussian likelihood for the growth index. We show that the constant $\gamma$ 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 $2.4\sigma -3.4\sigma$ tension level with constant $G_{\mathrm{eff}}$, depending on the parametrization. The results indicate that $G_{\mathrm{eff}}<G_N$ 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.

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• Cosmological parameters
• Large scale structure of the Universe