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Measuring local primordial non-Gaussianity from the clustering of DESI DR1 LRGs and QSOs

This paper presents the first measurement of primordial non-Gaussianity ( $f_{\mathrm{NL}}$ ) in configuration space using DESI DR1 LRG and QSO samples, yielding a joint constraint of $f_{\mathrm{NL}} = -3^{+12}_{-12}$ that demonstrates DESI's constraining power significantly exceeds previous large-scale structure surveys and approaches CMB sensitivity.

Original authors: Z. Brown, B. Levi, H. Randall, E. Chaussidon, R. Demina, A. G. Adame, S. Avila, V. Gonzalez-Perez, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, T. Claybaugh, A. Cuceu, A. de la Macorra, Biprateep Dey

Published 2026-06-24

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CC BY 4.0

Original authors: Z. Brown, B. Levi, H. Randall, E. Chaussidon, R. Demina, A. G. Adame, S. Avila, V. Gonzalez-Perez, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, T. Claybaugh, A. Cuceu, A. de la Macorra, Biprateep Dey, P. Doel, J. E. Forero-Romero, E. Gaztanaga, Satya Gontcho A Gontcho, G. Gutierrez, C. Hahn, K. Honscheid, D. Huterer, M. Ishak, R. Joyce, D. Kirkby, C. Lamman, M. Landriau, M. Manera, A. Meisner, R. Miquel, S. Nadathur, W. J. Percival, I. Perez-Rafols, A. Ross, G. Rossi, L. Samushia, E. Sanchez, M. Schubnell, J. Silber, D. Sprayberry, G. Tarle, B. A. Weaver, 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

Imagine the universe as a giant, expanding balloon. In the very first split second of its existence, this balloon didn't just inflate smoothly; it might have had tiny, random "bumps" or wrinkles in its surface. Scientists call these wrinkles primordial non-Gaussianity (or PNG for short).

For decades, the best way to look for these wrinkles was to study the Cosmic Microwave Background (CMB)—essentially the "baby photo" of the universe. But now, we have a new, powerful tool: the Dark Energy Spectroscopic Instrument (DESI). Think of DESI as a massive, high-speed camera that doesn't just take pictures, but takes detailed 3D maps of millions of galaxies and quasars (super-bright black holes) across the sky.

Here is what this paper did, explained simply:

1. The Goal: Finding the "Fingerprint" of the Big Bang

Scientists want to know if the early universe was perfectly smooth (Gaussian) or if it had those special, complex bumps (non-Gaussian). If the universe had these bumps, it would change how galaxies clump together today, much like how a rough surface causes water droplets to bead up differently than a smooth one.

The paper focuses on measuring a specific number, called $f_{NL}$ , which acts like a "bump meter."

If $f_{NL}$ is zero, the universe was smooth.
If $f_{NL}$ is a big number, the universe had complex, multi-field physics during its birth.

2. The Method: Counting Galaxy Friends

Instead of looking at the "baby photo" (CMB), the authors looked at the "adult photo" (the current distribution of galaxies). They used two specific groups of cosmic objects from the first year of DESI data:

LRGs (Luminous Red Galaxies): These are like the "elders" of the galaxy world—old, red, and bright.
QSOs (Quasars): These are the "teenagers"—very bright, energetic, and found further away (meaning we see them as they were younger).

The team used a clever algorithm (called ConKer) to measure the Two-Point Correlation Function (2pcf). In plain English, this is a way of counting how often galaxies are found at specific distances from each other. They asked: "Are galaxies clustering together more than we'd expect if the universe were perfectly smooth?"

3. The Challenge: The "Dirty Lens" Problem

Looking at the universe is tricky because our view is often distorted by things in our own neighborhood, like dust in space or the quality of the telescope's camera. In the paper, they call these imaging systematics.

Imagine trying to count how many people are in a stadium, but the lights are flickering in some sections and the seats are broken in others. You might think there are fewer people in the dark spots, but it's just the lights.

The Paper's Solution: They developed a new way to "clean the lens." They created a simulation of the universe and applied the same "dirty lens" effects to it. By comparing the messy simulation to the real data, they could mathematically subtract the errors caused by the telescope and dust, leaving only the true cosmic signal.

4. The Results: The Universe is Smooth (So Far)

After crunching the numbers on over 2 million galaxies and quasars, here is what they found:

The Measurement: The "bump meter" ( $f_{NL}$ ) read -3.
The Uncertainty: Because measurements always have a little wiggle room, the result is actually -3 plus or minus 12.
The Meaning: Since the range of possible values includes zero, the data suggests that the early universe was likely smooth. We haven't found evidence of those complex, multi-field "bumps" yet.

5. Why This Matters

This is a huge deal for two reasons:

It's a New Way of Looking: Previous studies mostly looked at the "Fourier space" (a mathematical way of looking at waves). This paper successfully measured it in "configuration space" (looking at actual distances between galaxies). It's like verifying a recipe by tasting the soup and checking the ingredients list separately; both methods now agree.
DESI is Powerful: Even though this is only the first year of data (DR1), the precision of DESI is so good that it is now competing with the best measurements from the Cosmic Microwave Background (the "baby photo").

The Bottom Line

The authors conclude that with the first year of DESI data, they have successfully measured the clustering of galaxies to look for signs of the universe's birth. They found no evidence of complex "bumps" in the early universe, but more importantly, they proved that DESI is sensitive enough to rival the best space telescopes in studying the very beginning of time. They are now ready to keep looking as more data comes in.

Technical Summary: Measuring Local Primordial Non-Gaussianity from DESI DR1 Clustering

Problem Statement
The nature of the inflationary epoch in the early Universe remains a primary open question in cosmology. While the Cosmic Microwave Background (CMB) has provided the most sensitive constraints on primordial non-Gaussianity (PNG) to date, Large Scale Structure (LSS) surveys offer a complementary and potentially competitive probe. PNG, parameterized by the local non-linearity parameter $f_{\text{NL}}$ , induces a scale-dependent bias in the clustering of tracers. However, measuring $f_{\text{NL}}$ in configuration space (the two-point correlation function, or 2pcf) is notoriously difficult due to contamination from imaging systematics. Variations in survey depth, dust extinction, and stellar density can induce angular density fluctuations that mimic the large-scale clustering signal of PNG. This paper addresses the challenge of extracting a robust $f_{\text{NL}}$ measurement from the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) while rigorously mitigating these systematic effects.

Methodology
The authors employ a simulation-based statistical framework to model the 2pcf monopole of Luminous Red Galaxies (LRGs) and Quasars (QSOs) from the DESI DR1 sample.

Data Processing: The analysis utilizes the ConKer algorithm to estimate the 2pcf. Tracers are mapped to a 3D Cartesian grid with weights ( $w_{\text{tot}}$ ) accounting for imaging systematics ( $w_{\text{sys}}$ ), catalog incompleteness ( $w_{\text{comp}}$ ), redshift failures ( $w_{\text{zfail}}$ ), and FKP weights ( $w_{\text{FKP}}$ ). The analysis covers the Northern and Southern Galactic Caps (NGC/SGC) for LRGs ( $0.4 < z < 1.1$ ) and QSOs ( $0.8 < z < 3.1$ ).
Theoretical Model: The model is entirely simulation-based, anchored on AbacusSummit high-resolution N-body simulations for the fiducial ( $f_{\text{NL}}=0$ ) case and "FastPM" simulations for the PNG dependence. The 2pcf is modeled as a linear interpolation between $f_{\text{NL}}=0$ and $f_{\text{NL}}=100$ realizations.
Bias and Universality: The model incorporates the linear galaxy bias ( $\tilde{b}_1$ ) and the PNG bias ( $b_\phi$ ). The relationship between these is governed by the Universality relation: $b_\phi = 2\delta_c(b_1 - p)$ , where $p$ is a tracer-dependent parameter. The analysis imposes Gaussian priors on $p$ : $p_{\text{LRG}} = 1.0 \pm 0.1$ and $p_{\text{QSO}} = 1.6 \pm 0.1$ .
Systematics Mitigation: A critical component of the methodology is the explicit modeling of imaging systematics. The authors introduce nuisance parameters ( $K^R_{\text{sys}}$ ) representing the fractional over- or under-application of imaging weights in specific survey regions (MzLS, (N)DEC, (S)DEC). These parameters are constrained via a simulation-based approach where the effect of varying weights on the 2pcf is pre-calculated and fit to a quadratic function.
Statistical Inference: A likelihood function is constructed using a $\chi^2$ statistic that includes the covariance matrix derived from 1000 EZ (effective Zel'dovich) mocks. The parameters of interest ( $f_{\text{NL}}$ and linear bias $b_1$ ) and seven nuisance parameters are sampled using Markov Chain Monte Carlo (MCMC). Baryon Acoustic Oscillation (BAO) scales ( $100 < s < 120 \, h^{-1}\text{Mpc}$ ) are masked to avoid non-linear modeling biases.

Key Results
The analysis yields the first measurement of $f_{\text{NL}}$ in the configuration space 2pcf using DESI data:

LRG Sample: The measurement yields $f_{\text{NL}} = -3^{+22}_{-21}$ at 68% confidence level (CL).
QSO Sample: The measurement yields $f_{\text{NL}} = 0^{+17}_{-16}$ at 68% CL.
Joint Constraint: Combining both tracer samples results in a joint constraint of $f_{\text{NL}} = -3^{+12}_{-12}$ at 68% CL.
Bias Parameters: The linear biases are constrained to $b_1 = 2.01 \pm 0.06$ for LRGs and $b_1 = 2.57 \pm 0.10$ for QSOs.
Systematics: The nuisance parameters governing imaging systematics ( $K_{\text{sys}}$ ) and the formation parameter $p$ remain largely consistent with their priors, indicating that the data does not strongly prefer deviations from the fiducial systematic models.

Significance and Claims
The paper claims three primary conclusions:

Robustness of Configuration-Space Analysis: The work demonstrates that a robust PNG study requires analysis in both Fourier and configuration spaces. While the effects of PNG differ in these domains, the consistency of these configuration-space results with previous Fourier-space analyses (Chaussidon et al. 2025) validates the approach.
Criticality of Systematics Mitigation: The study emphasizes that controlling imaging systematics is paramount for LSS PNG measurements. The agreement between this configuration-space result and independent Fourier-space results (which use different systematics mitigation strategies) serves as a strong validation of the pipeline's ability to handle survey incompleteness and angular density variations.
Constraining Power of LSS: The most significant claim is that LSS surveys are rapidly approaching the sensitivity of CMB probes. With only the first year of DESI data, the joint constraint ( $\sigma_{f_{\text{NL}}} \approx 12$ ) significantly exceeds previous LSS constraints and approaches the sensitivity of the Planck CMB measurement ( $\sigma_{f_{\text{NL}}} \approx 5$ ). The authors posit that the field has entered an era where late-time cosmological structure characterization will be a leading probe of primordial physics.

The results are consistent with the standard inflationary "slow-roll" model ( $f_{\text{NL}} \approx 0$ ) and do not show evidence for multi-field inflation scenarios within the current precision limits.