Further support for <i>S</i>8 increasing with effective redshift

ABSTRACT We previously reported an increasing trend in $S_8$ with effective redshift $z_{\textrm {eff}}$ based on $f \sigma _8(z)$ constraints over the redshift range $0 \lesssim z \lesssim 2$. Recently, independent studies presenting data that aligns with the expected trends have appeared. Here, we quantify the statistical significance of the increasing $S_8$ trends in these newer studies by fitting a linear model for the slope $\Delta \, S_8/\Delta \, z_{\textrm {eff}}$ and comparing to mock simulations. We find probabilities of $p = 0.0163$ and $p = 0.0185$, corresponding to approximately $2.1\sigma$ for each data set. The studies overlap in their use of DESI Legacy Survey data, but in one study the role of optical data is to mitigate systematics by removing contaminants from the pipeline. On the plausible assumption that correlations are negligible, we use Fisher’s method to combine the independent probabilities and obtain $p=0.0027$ ($2.8\sigma$). When we incorporate earlier findings, the combined statistical significance reaches between $3\sigma$ and $3.7\sigma$. Finally, we discuss how ‘scatter’ in $\sigma _8$/$S_8$ constraints from recent DESI full-shape galaxy clustering fits this picture at low statistical significance. This letter continues a series of studies initiated in 2020 that explore redshift-dependent $\Lambda$CDM parameters as an indication of model breakdown.