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 ∼3 σ 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 ΛCDM cosmology. In this work, we constrain S 8 using the high-purity CatNorth 1.5 million quasar candidate catalog and the Planck DR4 CMB lensing data across broad redshift ranges through autocorrelation 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 S 8 = 0.84 4 − 0.056 + 0.058 , consistent with the Planck 2018 CMB anisotropy constraints of S 8 = 0.834 ± 0.016 but lower than the 0.87 9 − 0.055 + 0.055 reported by a previous work using the Quaia quasar candidate catalog. However, for high-redshift faint quasars at z > 1.5, we find a lower value of S 8 = 0.72 4 − 0.054 + 0.058 , likely due to the sample incompleteness and/or the foreground contamination. Further tests on the volume-limited samples exhibit a consistent trend: S 8 = 0.83 5 − 0.049 + 0.053 for z 0.82 4 − 0.062 + 0.061 for 0.4 0.78 9 − 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.