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| Paper IPM / P / 18300 |
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In Adil et al.~(2023)~\cite{Adil:2023jtu}, we reported an increasing trend in $S_8$ with effective redshift $z_{\textrm{eff}}$ based on $f \sigma_8(z)$ constraints over the redshift range $0 \lesssim z \lesssim 2$, and predicted that this trend would be observable in independent datasets. Recently, the studies by Artis et al.~\cite{Artis:2024zag} and the ACT/DESI collaboration~\cite{ACT:2024nrz} appeared, presenting data that aligns with the expected trends. In this letter, we quantify the statistical significance of the increasing $S_8$ trends in~\cite{Artis:2024zag,ACT:2024nrz} by fitting a linear model to estimate the slope $\Delta\,S_8/\Delta\, z_{\textrm{eff}}$, and comparing the results to mock simulations. We find probabilities of $p = 0.0163$ and $p = 0.0185$, corresponding to approximately $2.1\sigma$ for each dataset. Using Fisherâs method to combine the independent probabilities, we obtain $p = 0.0027$ ($2.8\sigma$). When we incorporate our earlier findings~\cite{Adil:2023jtu}, 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 a breakdown in the standard cosmological model.
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