🔭 astrophysics

Constraining primordial non-Gaussianity from DESI DR1 quasars and Planck PR4 CMB Lensing

This paper presents the first measurement of local-type primordial non-Gaussianity using the cross-correlation of 1.2 million DESI DR1 spectroscopic quasars with Planck PR4 CMB lensing, achieving a constraint of $f_{\mathrm{NL}} = 2^{+28}_{-34}$ that improves upon previous limits by approximately 35% and demonstrates the statistical power of DESI for probing inflationary physics.

Original authors: Sofia Chiarenza, Alex Krolewski, Marco Bonici, Edmond Chaussidon, Roger de Belsunce, Will Percival, Jessica Nicole Aguilar, Steven Ahlen, Anton Baleato Lizancos, Davide Bianchi, David Brooks, Todd Cla

Published 2026-04-17

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Sofia Chiarenza, Alex Krolewski, Marco Bonici, Edmond Chaussidon, Roger de Belsunce, Will Percival, Jessica Nicole Aguilar, Steven Ahlen, Anton Baleato Lizancos, Davide Bianchi, David Brooks, Todd Claybaugh, Andrei Cuceu, Kyle Dawson, Axel de la Macorra, Peter Doel, Simone Ferraro, Andreu Font-Ribera, Jaime E. Forero-Romero, Enrique Gaztañaga, Satya Gontcho A Gontcho, Gaston Gutierrez, Hiram K. Herrera-Alcantar, Klaus Honscheid, Dragan Huterer, Mustapha Ishak, Dick Joyce, David Kirkby, Anthony Kremin, Ofer Lahav, Claire Lamman, Martin Landriau, Laurent Le Guillou, Michael Levi, Marc Manera, Paul Martini, Aaron Meisner, Ramon Miquel, Seshadri Nadathur, Jeffrey A. Newman, Gustavo Niz, Nathalie Palanque-Delabrouille, Claire Poppett, Francisco Prada, Ignasi Pérez-Ràfols, Graziano Rossi, Eusebio Sanchez, David Schlegel, Michael Schubnell, Hee-Jong Seo, Joseph Harry Silber, David Sprayberry, Gregory Tarlé, Benjamin Alan Weaver, Christophe Yèche, Rongpu Zhou, Hu 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: Hunting for a Cosmic Ghost

Imagine the universe as a giant, expanding balloon. When it was born in the Big Bang, it wasn't perfectly smooth; it had tiny, random bumps and ripples. Most of these ripples were "Gaussian," which is a fancy math way of saying they were perfectly random, like static on an old TV screen.

However, some theories about the very beginning of the universe (called Inflation) suggest that there might have been a tiny bit of "weirdness" or non-Gaussianity in those ripples. Think of it like baking a cake: if you mix the batter perfectly, the texture is uniform (Gaussian). But if you accidentally dropped a clump of unmixed flour in one spot, that's a "non-Gaussian" anomaly.

The goal of this paper is to find that "clump of flour." Scientists call this anomaly $f_{NL}$ . If they can measure it, it tells us exactly what kind of physics happened in the first fraction of a second after the Big Bang.

The Tools: A Cosmic Flashlight and a Giant Net

To find this tiny signal, the researchers used two massive tools:

DESI (The Net): The Dark Energy Spectroscopic Instrument is a robot telescope that can grab the "fingerprints" (spectra) of 5,000 galaxies or quasars at once. In this study, they used 1.2 million quasars.
- Analogy: Imagine quasars as incredibly bright lighthouses scattered across the universe. Because they are so bright, we can see them from very far away (high redshift), meaning we are looking back in time.
Planck (The Flashlight): The Planck satellite mapped the Cosmic Microwave Background (CMB), the afterglow of the Big Bang. Specifically, they used a map showing how gravity from all the matter in the universe bent the light from that afterglow (CMB Lensing).
- Analogy: Imagine looking at a streetlamp through a wavy glass window. The glass (matter in the universe) distorts the light. By studying the distortion, we can map where the glass is.

The Method: Cross-Referencing the Maps

The researchers didn't just look at the quasars alone or the CMB alone. They cross-correlated them.

The Problem: If you look at the quasars alone, "noise" from the telescope or the Earth's atmosphere can create fake patterns that look like the signal you are hunting. It's like trying to hear a whisper in a noisy room; you might think you heard a word, but it was just the wind.
The Solution: By comparing the map of the quasars (the lighthouses) with the map of the CMB distortion (the glass), they could filter out the noise. The "wind" (systematic errors) affects the telescope differently than it affects the CMB satellite. If a pattern shows up in both maps, it's likely real. If it only shows up in one, it's probably just noise.

The Innovation: Why This Paper is Special

Previous attempts to do this had two main problems:

Bad Data: They used "photometric" quasars (just pictures of light), which are like looking at the lighthouses through fog. It's hard to tell exactly where they are. This study used spectroscopic quasars (DESI DR1), which are like having a GPS coordinate for every single lighthouse. The data is much cleaner.
Old Maps: They used older CMB maps. This study used the Planck PR4 maps, which are like upgrading from a standard definition TV to 4K. The image is sharper, and the "static" (noise) is lower.

The Results: Finding the "Clump"

The team ran their analysis and asked: "Is there a signal of non-Gaussianity?"

The Answer: They found a signal, but it was very faint. Their best guess is that the "clump of flour" is zero, but the uncertainty is still quite large.
The Numbers: They measured a value of roughly 2, with a margin of error of about ±30.
- Translation: It's like guessing the weight of a feather. You might guess 2 grams, but your scale is so sensitive that the feather could actually weigh anywhere between -28 and +32 grams. Because the range includes zero, we can't say for sure the "clump" exists yet.
The Progress: Even though they didn't find a definitive "clump," they improved the precision of their guess by 35% compared to the previous best attempt. They narrowed the search area significantly.

The "Secret Sauce": Optimal Weighting

The paper also tested a new mathematical trick called Optimal Weighting.

Analogy: Imagine you are listening to a choir. Some singers are louder and clearer than others. Instead of listening to everyone equally, you turn up the volume on the clear singers and turn down the volume on the ones who are off-key or far away.
The researchers developed a way to "turn up the volume" on the quasars that are most likely to show the non-Gaussian signal (the high-redshift ones) and "turn down" the ones that are less useful.
Result: This trick improved their precision by another 5–10%, but because the data is still a bit "noisy," the biggest gain came from using the cleaner DESI data itself.

The Conclusion: A Stepping Stone

This paper is a victory lap for the DESI project. It proves that using high-quality spectroscopic data combined with CMB lensing is a powerful way to hunt for the physics of the early universe.

While they haven't found the "smoking gun" (a definitive detection of non-Gaussianity) yet, they have built a much better microscope. As DESI continues to map more of the sky in future years, the "noise" will drop, the "signal" will become clearer, and we might finally see that first clump of flour that tells us how the universe began.

In short: They used a sharper telescope and a cleaner map to look for a tiny cosmic anomaly. They didn't find it yet, but they got 35% closer than anyone else has before, proving that the next generation of data will likely crack the case.

1. Problem Statement

The primary goal of the paper is to constrain the amplitude of local-type primordial non-Gaussianity (PNG), parameterized by $f_{\text{NL}}$ . While the standard inflationary model predicts nearly Gaussian initial conditions ( $f_{\text{NL}} \sim \mathcal{O}(10^{-2})$ ), many multi-field inflation models predict larger deviations ( $f_{\text{NL}} \sim \mathcal{O}(1)$ ).

Current constraints from the CMB (Planck) are approaching the cosmic variance limit. Therefore, Large Scale Structure (LSS) offers the best path for improvement. Local PNG induces a scale-dependent bias in the clustering of tracers (like quasars) on very large scales ( $k \to 0$ ), enhancing the power spectrum as $\propto k^{-2}$ . However, measuring this signal is notoriously difficult due to:

Systematic uncertainties: Imaging systematics (e.g., dust, seeing, stellar density) can introduce spurious power on large scales, mimicking the PNG signal.
Noise: The signal is weak and dominated by noise on the largest scales.
Previous limitations: Previous analyses using photometric quasar samples (e.g., DESI Legacy Survey) suffered from significant systematic contamination and excess large-scale power in auto-correlations.

2. Methodology

The authors present the first measurement of $f_{\text{NL}}$ using the cross-correlation between spectroscopic quasars from DESI DR1 and Planck PR4 CMB lensing maps.

Data Sets

DESI DR1 Quasars: A spectroscopically confirmed sample of 1.2 million quasars ( $0.8 < z < 3.5$ $0.8 < z < 3.5$ ). The sample is divided into three tomographic redshift bins:
1. $0.8 < z < 2.1$ (856k objects)
2. $2.1 < z < 2.5$ (194k objects)
3. $2.5 < z < 3.5$ (171k objects)
Planck PR4 CMB Lensing: Utilizes the latest PR4 convergence ( $\kappa$ ) maps, which have $\sim 20\%$ lower noise than the 2018 release due to improved processing (NPIPE) and anisotropic filtering.

Analysis Pipeline

Estimator: The authors use a catalog-based pseudo- $C_\ell$ estimator (via NaMaster) rather than a pixelized approach. This avoids numerical instabilities in low-completeness pixels that previously caused excess large-scale power in auto-correlations.
Systematic Weights: They apply linear systematic weights (WEIGHT_IMLIN and WEIGHT_Linear) to correct for imaging systematics. Crucially, they validate these weights using 500 noiseless lognormal mocks. They found that while weights remove some power in auto-correlations (requiring correction), they do not significantly over-subtract signal in the cross-correlation ( $C_{\kappa g}$ ), allowing for a direct measurement without complex mode-correction.
Theoretical Modeling:
- They compute the angular cross-power spectrum $C_{\kappa g}^\ell$ without the Limber approximation (using Blast.jl) to accurately model the very large scales ( $\ell < 300$ ) where the PNG signal resides.
- The model includes contributions from number counts, magnification bias, redshift-space distortions (RSD), and the PNG-induced scale-dependent bias.
- The PNG bias is modeled via the relation $b_\Phi = 2\delta_c(b_1 - p)$ , testing two scenarios: $p=1.6$ (merger-dominated quasars) and $p=1.0$ (universality relation).
Optimal Weighting: The authors derive and test an optimal redshift weighting scheme ( $w_{\text{opt}} \propto (b(z)-p)$ ) to maximize the $f_{\text{NL}}$ signal-to-noise ratio.

3. Key Contributions

First Spectroscopic Cross-Correlation: This is the first $f_{\text{NL}}$ constraint derived from the cross-correlation of spectroscopically confirmed DESI quasars with CMB lensing. Spectroscopic samples have much higher purity than photometric ones, reducing systematic errors.
Robust Systematics Handling: By demonstrating that the cross-correlation is immune to the "excess large-scale power" seen in previous photometric auto-correlations, the authors establish a cleaner, more robust method for PNG constraints.
Validation of Weights: A rigorous validation using noiseless mocks confirmed that linear systematic weights do not spuriously remove cosmological signal in the cross-correlation, a critical step often overlooked.
Optimal Weighting Derivation: The paper provides a derivation for optimal redshift weights specifically for the CMB lensing-galaxy cross-correlation, showing a modest ( $\sim 5-10\%$ ) improvement in constraining power.

4. Results

The analysis covers the multipole range $4 < \ell < 300$ and a sky fraction of $\sim 20\%$ .

Fiducial Results (No Optimal Weights):
- For $p = 1.6$ : $f_{\text{NL}} = 2^{+28}_{-34}$
- For $p = 1.0$ : $f_{\text{NL}} = 6^{+20}_{-24}$
With Optimal Weights:
- For $p = 1.6$ : $f_{\text{NL}} = 19^{+25}_{-31}$
Comparison to Previous Work:
- These results improve constraints by $\sim 35\%$ compared to the previous analysis using the DESI Legacy Survey photometric quasars ( $\sigma_{f_{\text{NL}}} \approx 45$ ).
- The improvement is driven by the spectroscopic purity, the lower noise of Planck PR4, and the stable catalog-based estimator.
Bias Anomaly: The analysis reveals a tension in the third redshift bin ( $z > 2.5$ ), where the fitted bias amplitude is $\sim 30\%$ lower than expected ( $b_0 \approx 0.68$ ). However, the authors demonstrate that $f_{\text{NL}}$ constraints are robust to variations in the bias evolution model (constant vs. linear interpolation).
Robustness: The results remain consistent when varying the bias relation, removing the lowest multipole ( $\ell=6.5$ ), or freeing the primordial power spectrum parameters ( $A_s, n_s$ ).

5. Significance

Statistical Power: The study demonstrates that DESI quasars are powerful tracers for inflationary physics. Despite covering only $\sim 17-20\%$ of the sky, the high purity of the spectroscopic sample allows DESI to achieve constraints comparable to full-sky photometric surveys (like Quaia) but with significantly reduced systematic uncertainty.
Future Prospects: The paper highlights that while current constraints are still noise-dominated, future DESI data releases (covering more sky and deeper redshifts) combined with Stage-4 CMB experiments will push toward the $\sigma_{f_{\text{NL}}} < 1$ regime, potentially ruling out significant classes of inflationary models.
Methodological Benchmark: The successful application of catalog-based estimators and the validation of systematic weights in cross-correlations provide a blueprint for future high-precision LSS analyses.

In summary, this work represents a significant step forward in using LSS to probe the early universe, leveraging the unique strengths of the DESI spectroscopic survey and Planck PR4 data to deliver the most robust cross-correlation constraint on local non-Gaussianity to date.