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

Jin Qin, Xue-Bing Wu, Yuming Fu, Haojie Xu, Yuxuan Pang, Yun-Hao Zhang, Pengjie Zhang

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 $z<1.5$ yield $S_8 = 0.844^{+0.058}_{-0.056}$, consistent with the {\it Planck} 2018 CMB anisotropies constraints of $S_8=0.834\pm0.016$ but lower than the $0.879^{+0.055}_{-0.055}$ 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 $S_8=0.724^{+0.058}_{-0.054}$, likely due to the sample incompleteness and/or the foreground contamination. Further tests on the volume-limited samples exhibit a consistent trend: $S_8 = 0.835^{+0.053}_{-0.049}$ for $z < 2$, $0.824^{+0.061}_{-0.062}$ for $0.4 < z < 1.5$, and a lower value of $0.789^{+0.062}_{-0.062}$ 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.

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

Abstract

The parameter , a key probe of cosmic structure growth, exhibits a persistent 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 CDM cosmology. In this work, we constrain 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 yield , consistent with the {\it Planck} 2018 CMB anisotropies constraints of but lower than the reported by a previous work using the Quaia quasar candidate catalog. However, for high-redshift faint quasars at , we find a lower value of , likely due to the sample incompleteness and/or the foreground contamination. Further tests on the volume-limited samples exhibit a consistent trend: for , for , and a lower value of for the higher redshift range of . While future data may refine these results, our current measurements based on a large sample of quasar candidates show less evidence of the tension.
Paper Structure (11 sections, 20 equations, 21 figures, 2 tables)

This paper contains 11 sections, 20 equations, 21 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Data
  3. The CatNorth Quasar Candidate Catalog
  4. CMB Weak Lensing
  5. Methodology
  6. Selection Function
  7. Angular Power Spectrum Analysis
  8. Likelihood and Priors on Parameters
  9. Results and Discussion
  10. Conclusion
  11. Selection function

Figures (21)

  • Figure 1: The sky density map of the CatNorth quasar candidate catalog Fu_2024_CatNorth is shown in Galactic coordinates using the HEALPix framework 2005_Gorski_healpix. The map adopts a resolution parameter of $N_{\rm side} = 64$, corresponding to an area of 0.839 square degrees per pixel. Accordingly, the color bar is expressed in units of counts per 0.839 square degrees.
  • Figure 2: The apparent magnitude distribution of the CatNorth objects, where we mark the Gaia G-band magnitude limits of $\texttt{phot\_g\_mean\_mag} \leq 20.0$ and $\texttt{phot\_g\_mean\_mag} \leq 20.5$.
  • Figure 3: The Planck DR4 CMB lensing map is presented in Galactic coordinates using the HEALPix framework 2005_Gorski_healpix. This map has a resolution parameter of $N_{\rm side}=512$.
  • Figure 4: The selection function for the CatNorth catalog, without a magnitude cut, is presented in Galactic coordinates using the HEALPix framework with a resolution of $N_{\rm side} = 64$. Here, $S(\boldsymbol{\hat{n}}) = 0$ indicates the absence of data, while $S(\boldsymbol{\hat{n}}) = 1$ signifies complete data coverage. Significant incompleteness is evident in the Galactic plane and certain high Galactic latitude regions.
  • Figure 5: The normalized redshift distribution calibrated using the DIR method, for different subcatalogs in CatNorth.
  • ...and 16 more figures