Exploring the Growth-Index ($\gamma$) Tension with $\Lambda_{\rm s}$CDM

Recent observational analyses have revealed a significant tension in the growth index $\gamma$, which characterizes the growth rate of cosmic structures. Specifically, when treating $\gamma$ as a free parameter within $\Lambda$CDM framework, a combination of Planck and $f\sigma_8$ data yields $\gamma \approx 0.64$, in $\sim4\sigma$ tension with the theoretically expected value $\gamma \approx 0.55$ (assuming general relativity). This discrepancy, closely related to the $S_8$ tension, poses a new challenge to the standard cosmological model by suggesting that it predicts an excessive growth of structure. In this work, we demonstrate that the $\Lambda_{\rm s}$CDM framework (featuring a rapid sign-switching cosmological constant (mirror AdS-to-dS transition) in the late universe at redshift $z_\dagger \sim 2$) can simultaneously alleviate the $\gamma$, $H_0$, and $S_8$ tensions. We also examined a scenario with fixed $z_\dagger = 1.7$, previously identified as a sweet spot for alleviating multiple major cosmological tensions (including those in $H_0$, $M_B$, and $S_8$) finding that it completely eliminates both the $\gamma$ and $H_0$ tensions, although it is statistically disfavored by our dataset combinations. Our findings suggest that $\Lambda_{\rm s}$CDM is a promising model, providing a potential unified resolution to multiple major cosmological tensions.