Quantifying the S 8 tension with the Redshift Space Distortion data set

One problem of the $\Lambda$CDM model is the tension between the $S_8$ found in Cosmic Microwave Background (CMB) experiments and the smaller one obtained from large-scale observations in the late Universe. The ${\sigma }_8$ quantifies the relatively high level of clustering. Likelihood analyses of the Redshift Space Distortion (RSD) selected data set yields: $S_8=0.700_{-0.037}^{+0.038}$. The fit has $3\sigma$ tension with the Planck 2018 results. With Gaussian processes method a model-independent reconstructions of the growth history of matter in-homogeneity is studied. The fit yields $S_8=0.707_{-0.085}^{+0.085},0.701_{-0.089}^{+0.089}$, and $0.731_{-0.062}^{+0.063}$ for different kernels. The tension reduces and being smaller then $1.5\sigma$. With future measurements the tension may be reduced, but the possibility the tension is real is a plausible situation.