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One of the most prominent challenges to the standard Lambda cold dark matter($\Lambda$CDM) cosmology is the tension between the structure growth parameter$S_8$ constrained by the cosmic microwave background (CMB) data and the smallerone suggested by the cosmic shear data. Recent studies show that, for$\Lambda$CDM cosmology, redshift-space distortion (RSD) data also prefers asmaller $S_8$ that is $\sim 2$-$3\sigma$ lower than the CMB value, but theresult is sensitive to the cosmological model. In the present work we updatethe RSD constraint on $S_8$ with the most up-to-date RSD data set where thecorrelation between data points are properly taken into account. To reduce themodel dependence, we add in our Monte Carlo Markov Chain calculation the mostup-to-date data sets of Type Ia supernovae (SN) and baryon acousticoscillations (BAO), whose correlation with RSD is also taken into account, toconstrain the background geometry. For $\Lambda$CDM cosmology we find $S_8=0.812 \pm 0.026$, which is $\sim 2\sigma$ larger than previous studies, andhence is consistent with the CMB constraint. By replacing $\Lambda$CDM with theParameterization based on cosmic Age (PAge), an almost model-independentdescription of the late universe, we find that the RSD + SN + BAO constraint on$S_8$ is insensitive to the cosmological model.

The $S_8$ Tension in Light of Updated Redshift-Space Distortion Data and PAge Approximation