$S_8$ increases with effective redshift in $\Lambda$CDM cosmology

Understand

Hubble constant $H_0$ and weighted amplitude of matter fluctuations $S_8$ determinations are biased to higher and lower values, respectively, in the late Universe with respect to early Universe values inferred by the Planck collaboration within flat $\Lambda$CDM cosmology.

• If these anomalies are physical, i.e.
• not due to systematics, they naively suggest that $H_0$ decreases and $S_8$ increases with effective redshift.
• Here, subjecting matter density today $\Omega_{m}$ to a prior, corresponding to a combination of Planck CMB and BAO data, we perform a consistency test of the Planck-$\Lambda$CDM cosmology and show that $S_8$ determinations from $f \sigma_8(z)$ constraints increase with effective redshift.