[Paper Review] Further support for $S_8$ increasing with effective redshift

Özgür Akarsu, Eoin Ó Colgáin+2 more|arXiv (Cornell University)|Oct 30, 2024

Stochastic processes and financial applications6 citations

TL;DR

The paper quantifies the statistical significance of an increasing S8 trend with effective redshift using independent datasets (Artis et al. 2024 and Qu et al. 2024) and combines them with earlier results to indicate a ~3σ signal of redshift-dependent S8.

ABSTRACT

In Adil et al. 2023, we reported an increasing trend in $S_8$ with effective redshift $z_{ extrm{eff}}$ based on $f σ_8(z)$ 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. and the ACT+DESI collaboration appeared, presenting data that aligns with the expected trends. In this letter, we quantify the statistical significance of the increasing $S_8$ trends in recent studies by fitting a linear model to estimate the slope $Δ\,S_8/Δ\, z_{ extrm{eff}}$, and comparing the results to mock simulations. We find probabilities of $p = 0.0163$ and $p = 0.01893$, corresponding to approximately $2.1σ$ for each dataset. Using Fisher's method to combine the independent probabilities, we obtained $p=0.0027$ ($2.8 σ$). When we incorporate our earlier findings, the combined statistical significance reaches between $3σ$ and $3.7σ$. Finally, we discuss how ``scatter" in $σ_8$/$S_8$ 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 $Λ$CDM parameters as an indication of a breakdown in the standard cosmological model.

Motivation & Objective

• Motivate redshift-dependent tests of LambdaCDM parameters to identify potential model breakdowns.
• Quantify the trend of S8 with effective redshift in independent, high-quality datasets.
• Combine results across datasets to assess the overall statistical significance of the trend.
• Discuss implications for cosmology and the robustness of the LambdaCDM framework.

Proposed method

• Fit a linear model to S8 versus z_eff to estimate the slope Delta S8 / Delta z_eff.
• Generate 100,000 mock realizations by resampling S8 with its errors to compute the null distribution of slopes.
• Compute p-values for each dataset from mocks and convert to Gaussian significance.
• Combine independent p-values using Fisher’s method to obtain a joint significance.
• Benchmark the trend against Adil et al. (2023) and discuss implications for Omega_m evolution.

Experimental results

Research questions

• RQ1 Does S8 exhibit a statistically significant increase with effective redshift across independent datasets?
• RQ2 What is the estimated slope Delta S8 / Delta z_eff for each dataset and jointly?
• RQ3 How does the observed trend compare with expectations from Planck-LambdaCDM and potential systematics?
• RQ4 Is there evidence for redshift dependence in Omega_m that could accompany the S8 trend?

Key findings

• For Artis et al. (2024) data, the slope is m = 0.18^{+0.08}_{-0.09}, corresponding to about 2σ away from a constant S8.
• For Qu et al. (2024) data, the slope is m = 0.59^{+0.29}_{-0.28}, corresponding to about 2.1σ away from a constant S8.
• Mock realizations yield p = 0.0163 for Artis et al. (2024) and p = 0.0185 for Qu et al. (2024), each ~2.1σ significance.
• Fisher’s method combining the two independent datasets gives p = 0.0027 (~2.8σ).
• Including Adil et al. (2023) results raises the combined significance to between 3σ and 3.7σ.
• The combined analysis places the redshift-dependent S8 trend at roughly 3σ across three independent datasets.