Testing Scale-Dependent Suppression of Structure Growth in the Linear Regime

We investigate recent reports of a suppression in the growth rate of cosmic structures inferred from analyses of the $[f\sigma_8](z)$ dataset. To address this issue, we explore the hypothesis that the evolution of matter clustering is more accurately described within the framework of scale-dependent modified gravity. We perform a joint analysis of $[f\sigma_8](z)$, cosmic chronometer $H(z)$ measurements, luminosity distance data, and CMB observations using Markov Chain Monte Carlo techniques to constrain the parameters of a scale-dependent cosmological model and investigate its impact on the evolution of $[f\sigma_8](z)$. Our results indicate that the suppression of the growth rate of large-scale structures is more pronounced during the matter-dominated era than in the dark-energy-dominated epoch. We find evidence for scale-dependent growth at a statistical significance of $2.2\, \sigma$. In addition, we constrain the $S_8$ parameter and find it to be consistent with the value inferred from the CMB observations of the Planck Collaboration. Overall, our analysis shows that $k$-dependent growth models provide a viable explanation for the observed clustering of matter without exacerbating the current cosmological tensions.