Paper
Exploring the $S_8$ Tension: Insights from the CatNorth 1.5-Million Quasar Candidates
Authors
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.09457v1</id>\n <title>Exploring the $S_8$ Tension: Insights from the CatNorth 1.5-Million Quasar Candidates</title>\n <updated>2026-03-10T10:13:01Z</updated>\n <link href='https://arxiv.org/abs/2603.09457v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.09457v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='astro-ph.CO'/>\n <published>2026-03-10T10:13:01Z</published>\n <arxiv:comment>24 pages, 21 figures, 2 tables, accepted by APJ</arxiv:comment>\n <arxiv:primary_category term='astro-ph.CO'/>\n <author>\n <name>Jin Qin</name>\n </author>\n <author>\n <name>Xue-Bing Wu</name>\n </author>\n <author>\n <name>Yuming Fu</name>\n </author>\n <author>\n <name>Haojie Xu</name>\n </author>\n <author>\n <name>Yuxuan Pang</name>\n </author>\n <author>\n <name>Yun-Hao Zhang</name>\n </author>\n <author>\n <name>Pengjie Zhang</name>\n </author>\n </entry>"
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