Exploring the growth index γL: Insights from different CMB dataset combinations and approaches

In this study we investigate the growth index γL, which characterizes the growth of linear matter perturbations, while analysing different cosmological datasets. We compare the approaches implemented by two different patches of the cosmological solver CAMB: MGCAMB and CAMB_GAMMAPRIME_GROWTH. In our analysis we uncover a deviation of the growth index from its expected ΛCDM value of 0.55 when utilizing the Planck dataset, both in the MGCAMB case and in the CAMB_GAMMAPRIME_GROWTH case, but in opposite directions. This deviation is accompanied by a change in the direction of correlations with derived cosmological parameters. However, the incorporation of cosmic microwave background lensing data helps reconcile γL with its Λ-cold dark matter value in both cases. Conversely, the alternative ground-based telescopes Atacama Cosmology Telescope and South Pole Telescope consistently yield growth index values in agreement with γL ¼ 0.55. We conclude that the presence of the Alens problem in the Planck dataset contributes to the observed deviations, underscoring the importance of additional datasets in resolving these discrepancies.