Implications of a high growth index on the variation of G

A recent determination of the growth index indicates a value significantly higher than the ΛCDM prediction, suggesting that alternative scenarios to ΛCDM may be required. In this work, we investigate whether a time-varying Newton's constant, GN, can account for such a high growth index, γ=0. 0630. 025. Adopting a phenomenological approach, we study two parameterizations of the effective gravitational coupling, G ₄₅₅, 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 ₄₅₅, depending on the parametrization. The results indicate that G ₄₅₅