Quantifying the $S_8$ tension and evidence for interacting dark energy from redshift-space distortion measurements

In recent years, Cosmic Microwave Background (CMB) observations, Weak Lensing surveys, and $f{\sigma }_8(z)$ measurements from Redshift-Space Distortions (RSD) have revealed a significant ($\sim$3$-$5$\sigma$) discrepancy in the inferred value of the matter clustering parameter $S_8$. In this work, we investigate the implications of RSD for a cosmological framework postulating an interaction between Dark Energy (DE) and Dark Matter (DM). We explore scenarios where DM can transfer energy-momentum to DE or vice versa. The energy-momentum flow is characterized by the strength and the sign of the coupling parameter $\xi$. Our baseline analysis combines RSD measurements with the latest data from Baryon Acoustic Oscillations (BAO) observed by DESI, Type Ia Supernovae from the PantheonPlus sample, and CMB data from Planck. We demonstrate that RSD measurements provide significant additional information imposing new and strong upper bounds on possible interaction in the dark sector. Models with $\xi >0$ can effectively alleviate the tension in $S_8$, presenting them as compelling alternatives.