S 8 increases with effecti v e redshift in Λ CDM cosmology

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 Λ CDM cosmology. If these anomalies are physical, that is, not due to systematics, they naively suggest that H 0 decreases and S 8 increases with ef fecti ve redshift. Here, subjecting matter density today Ωm to a prior, corresponding to a combination of Planck CMB and BAO data, we perform a consistency test of the Planck - Λ CDM cosmology and show that S 8 determinations from f σ8 ( z) constraints increase with ef fecti ve redshift. Due to the redshift evolution, a ∼3 σtension in the S 8 parameter with Planck at lower redshifts remarkably becomes consistent with Planck within 1 σat high redshifts. This provides corroborating support for an S 8 discrepancy that is physical in origin. We further confirm that the flat Λ CDM model is preferred o v er a theoretically ad hoc model with a jump in S 8 at a given redshift. In the absence of the CMB + BAO Ωm prior, we find that > 3 σtensions with Planck in low-redshift data are ameliorated by shifts in the parameters in high-redshift data. Results here and elsewhere suggest that the Λ CDM cosmological parameters are redshift dependent. Fitting parameters that evolve with redshift is a recognizable hallmark of model breakdown.