Exploring the $S_8$ Tension: Insights from the CatNorth 1.5-Million Quasar Candidates

Abstract: The parameter $S_8$, a key probe of cosmic structure growth, exhibits a persistent $\sim3σ$ tension between high-redshift measurements from cosmic microwave background (CMB) anisotropies and low-redshift weak gravitational lensing observations. This discrepancy may indicate either unaccounted systematic effects or new physics beyond the standard $Λ$CDM cosmology. In this work, we constrain $S_8$ using the high purity CatNorth 1.5 million quasar candidate catalog and the {\it Planck} DR4 CMB lensing data across the broad redshift ranges through auto-correlation and cross-correlation analyses. To address the spatial incompleteness, we develop a machine-learning-based selection function that effectively suppresses the systematics-induced power spectrum excess on large scales. Our robust low-redshift measurements at $z&lt;1.5$ yield $S_8 = 0.844<sup>{+0.058}_{-0.056}$, consistent with the {\it Planck} 2018 CMB anisotropies constraints of $S_8=0.834\pm0.016$ but lower than the $0.879<sup>{+0.055}_{-0.055}$ reported by a previous work using the Quaia quasar candidate catalog. However, for high-redshift faint quasars at $z&gt;1.5$, we find a lower value of $S_8=0.724<sup>{+0.058}_{-0.054}$, likely due to the sample incompleteness and/or the foreground contamination. Further tests on the volume-limited samples exhibit a consistent trend: $S_8 = 0.835<sup>{+0.053}_{-0.049}$ for $z &lt; 2$, $0.824<sup>{+0.061}_{-0.062}$ for $0.4 < z < 1.5$, and a lower value of $0.789<sup>{+0.062}_{-0.062}$ for the higher redshift range of $1.5 < z < 2.5$. While future data may refine these results, our current measurements based on a large sample of quasar candidates show less evidence of the $S_8$ tension.