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Cosmology from Planck CMB Lensing and DESI DR1 Quasar Tomography

This paper presents a high-significance cross-correlation analysis of over 1.2 million DESI DR1 quasars and Planck PR4 CMB lensing maps to constrain the amplitude of matter fluctuations at high redshifts, finding a $1.5\sigma$ tension with standard $\Lambda$ CDM predictions while also deriving a sound-horizon-free measurement of the Hubble constant.

Original authors: R. de Belsunce, A. Krolewski, S. Chiarenza, E. Chaussidon, S. Ferraro, B. Hadzhiyska, C. Ravoux, N. Sailer, G. Farren, A. Tamone, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, T. Claybaugh, A. Cuceu, A

Published 2026-06-08

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: R. de Belsunce, A. Krolewski, S. Chiarenza, E. Chaussidon, S. Ferraro, B. Hadzhiyska, C. Ravoux, N. Sailer, G. Farren, A. Tamone, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, T. Claybaugh, A. Cuceu, A. de la Macorra, J. Della Costa, Biprateep Dey, P. Doel, A. Font-Ribera, J. E. Forero-Romero, E. Gaztañaga, S. Gontcho A Gontcho, G. Gutierrez, J. Guy, H. K. Herrera-Alcantar, K. Honscheid, M. Ishak, R. Joyce, S. Juneau, R. Kehoe, D. Kirkby, T. Kisner, A. Kremin, O. Lahav, A. Lambert, C. Lamman, M. Landriau, L. Le Guillou, M. E. Levi, M. Manera, P. Martini, A. Meisner, R. Miquel, S. Nadathur, G. Niz, N. Palanque-Delabrouille, W. J. Percival, F. Prada, I. Pérez-Ràfols, A. J. Ross, G. Rossi, E. Sanchez, D. Schlegel, M. Schubnell, H. Seo, J. Silber, D. Sprayberry, G. Tarlé, B. A. Weaver, R. Zhou, H. Zou

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Mapping the Invisible Web

Imagine the universe as a giant, invisible spiderweb made of dark matter. We can't see this web directly, but we know it's there because it has gravity. Just like a heavy rock placed on a trampoline bends the fabric, this invisible web bends the path of light traveling through space.

This paper is about two teams of astronomers working together to measure how "clumpy" or dense this invisible web is at different times in the universe's history. They are trying to answer a simple question: Is the universe growing the way our best theories say it should?

The Two Tools: A Flashlight and a Mirror

To do this, the researchers combined data from two very different cosmic tools:

The Flashlight (DESI Quasars):
Think of quasars as incredibly bright, ancient lighthouses scattered across the universe. The Dark Energy Spectroscopic Instrument (DESI) is like a super-powerful camera that took a picture of over 1.2 million of these lighthouses. Because these lighthouses are so far away, looking at them is like looking back in time. The researchers sorted these lighthouses into three "time bins" (groups based on how far away they are), looking at times when the universe was roughly 3 to 10 billion years old.
The Mirror (Planck CMB Lensing):
The Cosmic Microwave Background (CMB) is the "afterglow" of the Big Bang—the oldest light in the universe. As this light travels toward us, it passes through that invisible dark matter web. The web acts like a distorted mirror, bending the light slightly. The Planck satellite mapped these distortions. This is called "lensing." It's like looking at a funhouse mirror; the reflection tells you about the shape of the glass (the dark matter) even if you can't see the glass itself.

The Experiment: Matching the Reflections

The researchers performed a "cross-correlation." Imagine you have a map of where the lighthouses (quasars) are, and a separate map of how the funhouse mirror (CMB light) is distorted.

If the lighthouses are sitting right on top of the heavy parts of the invisible web, the mirror distortion should be strongest in those same spots. By comparing the two maps, the team could measure how much the universe's structure has grown over time.

The Result: They found a very strong match between the two maps. The signal was so clear that it was detected with a "signal-to-noise" ratio of 21.7. In everyday terms, this is like hearing a whisper in a quiet room when you were expecting a shout in a noisy stadium. It's a very confident detection.

The Findings: Is the Universe Growing Too Fast?

The main goal was to measure the "amplitude of matter fluctuations" (how clumpy the universe is). In cosmology, this is often summarized by a number called $S_8$ .

The Prediction: The standard model of the universe (called $\Lambda$ CDM), based on the very first light of the universe (the CMB), predicts a specific value for how clumpy the universe should be today.
The Measurement: The researchers measured the clumpiness using their quasar and lensing data.
The Comparison: Their measurement was slightly higher than the prediction—about 1.5 times the standard deviation (or 1.5 sigma) higher.

What does this mean?
Imagine you are baking a cake based on a recipe (the standard model). The recipe says the cake should rise to exactly 10 inches. You bake it, and it rises to 10.5 inches.

Is the recipe wrong? Maybe.
Is your oven just a little hotter? Maybe.
Is it a fluke? Possibly.

In science, a "1.5 sigma" difference is interesting, but it's not enough to say the recipe is definitely broken. It's like a "mild tension." The paper concludes that while their result is a bit higher than expected, it is consistent with the standard model given the current size of the error bars. They did not find definitive proof that the universe is behaving differently than we thought.

A Bonus Discovery: Measuring the Speed of the Universe's Expansion

The paper also used this data to measure the Hubble Constant ( $H_0$ ), which is the rate at which the universe is expanding.

Usually, measuring this rate is tricky because it depends on knowing the size of a "standard ruler" (the sound horizon) from the early universe. However, this team found a clever workaround. They looked at a different feature in the data—the "turnover" point where the distribution of matter changes from smooth to clumpy. This feature acts like a ruler that doesn't depend on the early universe's sound waves.

Using this method, they calculated the expansion rate to be roughly 69.1 km/s/Mpc.

This number sits comfortably in the middle of the two main camps of scientists: those who measure the early universe (who get a lower number) and those who measure nearby stars (who get a higher number).
Their result agrees well with other recent measurements, suggesting that perhaps the "Hubble Tension" (the disagreement between different methods) might be resolved or is less severe than previously feared.

Summary

What they did: They mapped 1.2 million ancient lighthouses (quasars) and compared them to distortions in the oldest light in the universe (CMB lensing).
What they found: The universe is clumpy, and the amount of clumpiness they measured is slightly higher than the "standard recipe" predicts, but not enough to declare the recipe wrong.
Why it matters: It confirms that our current understanding of gravity and the universe's structure holds up even when looking at very distant, ancient objects. It also provides a new, independent way to measure how fast the universe is expanding, which helps settle debates about the universe's age and fate.

The authors emphasize that as they get more data in the future (from DESI's next data releases), these measurements will become even sharper, potentially revealing if that "mild tension" is just a fluke or a sign of new physics.

Technical Summary: Cosmology from Planck CMB Lensing and DESI DR1 Quasar Tomography

Problem and Motivation
The standard $\Lambda$ CDM cosmological model predicts the amplitude of matter clustering, $\sigma_8$ , with high precision when conditioned on Cosmic Microwave Background (CMB) primary anisotropy data. However, various late-time probes, including weak lensing and CMB lensing cross-correlations, have reported mild tensions ( $\sim 1-3\sigma$ ) regarding the growth of structure, often parameterized by $S_8 \equiv \sigma_8(\Omega_m/0.3)^{0.5}$ . While some analyses find consistency with primary CMB predictions, others suggest a lower amplitude of structure. To address these discrepancies, it is crucial to measure the growth of structure at high redshifts ( $z > 1$ ) using large, spectroscopically confirmed samples that minimize uncertainties in redshift distributions and interloper contamination. This paper presents a measurement of the amplitude of matter fluctuations using the largest spectroscopic quasar sample to date at high redshift, cross-correlated with CMB lensing maps.

Methodology
The authors perform a tomographic analysis using data from two primary sources:

DESI DR1 Quasar Sample: A spectroscopically confirmed sample of 1,223,391 quasars covering $0.8 \le z \le 3.5$ over $7,200 \text{ deg}^2$ . The sample is divided into three redshift bins centered at effective redshifts $z_{\text{eff}} = 1.44, 2.27,$ and $2.75$. The analysis employs linear imaging systematic weights to correct for observational effects, avoiding the power suppression on large scales associated with non-linear Random Forest weights used in previous studies.
Planck PR4 CMB Lensing: The analysis utilizes the Planck PR4 (NPIPE) CMB lensing convergence ( $\kappa$ ) maps, which offer improved signal-to-noise compared to previous releases.

The core of the methodology involves measuring the angular power spectra: the auto-correlation of the quasar density field ( $C_{gg}$ ) and the cross-correlation between the quasar density and CMB lensing convergence ( $C_{g\kappa}$ ). These are estimated using the NaMaster algorithm to compute pseudo- $C_\ell$ spectra, which are then deconvolved from the survey mask using a mode-coupling matrix.

The theoretical modeling employs a hybrid approach combining fits to N-body simulations and Convolutional Lagrangian Effective Field Theory (CLEFT). The model includes:

Linear and non-linear bias terms ( $b_1, b_2, b_s$ ).
Magnification bias ( $s_\mu$ ).
Redshift-space distortions (RSD).
Shot noise, which is analytically marginalized.

The likelihood analysis uses a multi-variate Gaussian likelihood with a covariance matrix derived from Gaussian analytic approximations. To break the degeneracy between $\Omega_m$ and $\sigma_8$ , the authors incorporate a prior on $\Omega_m$ derived from DESI DR1 (and DR2) Baryon Acoustic Oscillation (BAO) measurements. The analysis is blinded at the likelihood level, with validation performed on Gaussian mocks and AbacusSummit N-body simulations to ensure parameter recovery and robustness against systematics such as fiber assignment effects and the angular integral constraint.

Key Contributions

Largest High- $z$ Spectroscopic Sample: This work utilizes the largest spectroscopic quasar sample to date for CMB lensing cross-correlations, providing a high-density, high-purity tracer sample in the matter-dominated regime ( $0.8 \le z \le 3.5$ ).
Robust Systematic Control: By utilizing spectroscopic redshifts and linear systematic weights, the analysis eliminates errors from redshift distribution uncertainties and minimizes large-scale power loss from imaging systematics.
Sound-Horizon-Free $H_0$ Measurement: The paper combines the quasar-CMB lensing cross-correlation with CMB lensing auto-spectra from Planck PR4 and the Atacama Cosmology Telescope (ACT DR6) to perform a measurement of the Hubble constant ( $H_0$ ) that is independent of the sound horizon scale, relying instead on the matter-radiation equality scale ( $k_{\text{eq}}$ ).

Results

Detection Significance: The cross-correlation between Planck PR4 lensing maps and the DESI DR1 quasar sample is detected with a signal-to-noise ratio (SNR) of 21.7. The quasar auto-correlation is detected at an SNR of 27.2 for the joint analysis of all redshift bins.
Growth of Structure Constraints:
- Using the joint analysis of all redshift bins and a DESI DR1 BAO prior, the authors constrain the amplitude of matter fluctuations to $\sigma_8 = 0.929^{+0.059}_{-0.074}$ and $S_8 = 0.922^{+0.059}_{-0.073}$ .
- These results are approximately $1.5\sigma$ higher than predictions from $\Lambda$ CDM fits to Planck PR4 primary CMB data.
- When restricting the analysis to linear theory (fixing higher-order biases and marginalizing over fewer nuisance parameters), the tension with primary CMB predictions reduces to $\sim 1\sigma$ , yielding $S_8 = 0.859 \pm 0.048$ .
- The authors note that while their constraints are higher than some galaxy lensing measurements, they are consistent with the "full modeling" results from the DESI DR1 QSO power spectrum analysis.
Hubble Constant: The sound-horizon-free measurement yields $H_0 = 69.1^{+2.2}_{-2.6} \text{ km s}^{-1}\text{Mpc}^{-1}$ (using DESI DR1 BAO priors) and $H_0 = 68.5 \pm 1.8 \text{ km s}^{-1}\text{Mpc}^{-1}$ (using DESI DR2 BAO priors). These values are in agreement with late-time distance ladder measurements (e.g., SH0ES, CCHP) and primary CMB constraints within $1-2\sigma$ .

Significance and Claims
The paper claims to provide a robust measurement of structure growth at high redshifts using a sample that is better characterized and has higher purity than previous photometric or target-selected quasar samples. The authors state that their results do not find conclusive evidence for a departure from $\Lambda$ CDM, noting that the observed tension with primary CMB predictions ( $\sim 1.5\sigma$ ) is reduced to $\sim 1\sigma$ when using linear theory fits. They emphasize that the current error bars are still too large to definitively support or rule out an " $S_8$ tension." The work serves as a proof of concept for using high-redshift spectroscopic quasars as tracers for CMB lensing, with the authors noting that future DESI data releases (Year 5) will significantly shrink error bars and further stress-test the $\Lambda$ CDM model in this high-redshift regime. The sound-horizon-free $H_0$ measurement is presented as a complementary probe to standard ruler methods, leveraging the turnover scale of the matter power spectrum.