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The DESI DR1 Peculiar Velocity Survey: growth rate measurements from galaxy and momentum correlation functions

Using the largest peculiar velocity and bright galaxy catalogues to date from DESI DR1, this study presents a joint analysis of velocity and density correlations to measure the growth rate of structure ( $f\sigma_8$ ) and the gravitational growth index ( $\gamma_L$ ), finding results consistent with General Relativity and $\Lambda$ CDM cosmology.

Original authors: R. J. Turner, C. Blake, F. Qin, J. Aguilar, S. Ahlen, A. J. Amsellem, J. Bautista, S. BenZvi, D. Bianchi, D. Brooks, A. Carr, E. Chaussidon, T. Claybaugh, A. Cuceu, A. de la Macorra, P. Doel, K. Dougl

Published 2026-07-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: R. J. Turner, C. Blake, F. Qin, J. Aguilar, S. Ahlen, A. J. Amsellem, J. Bautista, S. BenZvi, D. Bianchi, D. Brooks, A. Carr, E. Chaussidon, T. Claybaugh, A. Cuceu, A. de la Macorra, P. Doel, K. Douglass, S. Ferraro, A. Font-Ribera, J. E. Forero-Romero, E. Gaztañaga, S. Gontcho A Gontcho, G. Gutierrez, J. Guy, H. K. Herrera-Alcantar, K. Honscheid, C. Howlett, D. Huterer, M. Ishak, R. Joyce, R. Kehoe, A. G. Kim, D. Kirkby, A. Kremin, O. Lahav, Y. Lai, C. Lamman, M. Landriau, L. Le Guillou, A. Leauthaud, M. E. Levi, M. Manera, A. Meisner, R. Miquel, J. Moustakas, A. Muñoz-Gutiérrez, S. Nadathur, N. Palanque-Delabrouille, W. J. Percival, C. Poppett, F. Prada, I. Pérez-Ràfols, C. Ross, G. Rossi, K. Said, E. Sanchez, D. Schlegel, M. Schubnell, J. Silber, D. Sprayberry, G. Tarlé, B. A. Weaver, P. Zarrouk, 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, invisible ocean. Most of the time, this ocean is flowing smoothly, expanding outward like a balloon being blown up. But sometimes, the water gets choppy. Clumps of matter—galaxies—pull on each other with gravity, creating little whirlpools and currents that make galaxies move a bit faster or slower than the smooth expansion would predict. These extra, wobbly movements are called "peculiar velocities."

A team of astronomers, led by R. J. Turner, decided to map these cosmic currents using the Dark Energy Spectroscopic Instrument (DESI). They didn't just look at where galaxies are; they measured how fast they are actually moving through space, independent of the universe's expansion. Think of it like trying to figure out how strong the wind is by watching how much a kite sways, rather than just looking at how high it flies.

The Big Discovery: How Fast is the Universe Growing?

The main goal of this study was to measure a specific number called $f\sigma_8$ . You can think of this number as the "growth rate" of the universe's structure. It tells us how quickly the cosmic clumps (galaxies and dark matter) are getting bigger and pulling together due to gravity.

Using a massive new dataset—the largest of its kind ever assembled, containing over 415,000 galaxy positions and more than 76,000 measured peculiar velocities—the team found that the growth rate is $0.391^{+0.080}_{-0.081}$ .

To put this in perspective, they compared their result to the "standard recipe" for the universe (known as the Planck+ $\Lambda$ CDM model). Their measurement fits right in with that recipe, within a margin of error of about one standard deviation. In other words, the universe is growing exactly as the standard model of gravity (General Relativity) predicts it should.

The Detective Work: Three Ways to Solve the Case

The researchers didn't just use one trick to find this number; they used three different detective methods to make sure they weren't being fooled:

The Correlation Function Method: This is the main focus of the paper. They looked at how pairs of galaxies and their velocities are related to each other across different distances, like counting how often two friends are standing next to each other at a party.
The Power Spectrum Method: A different way of looking at the data, focusing on the patterns of waves in the distribution of galaxies.
The Maximum-Likelihood Method: A statistical approach that finds the most probable explanation for the data.

When they combined the results from all three methods, they got an even sharper picture: a consensus growth rate of $0.4497 \pm 0.0548$ at a specific cosmic time (redshift $z = 0.07$ ). This combined result is a very strong match for the predictions of General Relativity.

What They Ruled Out (and What They Didn't)

The paper is careful to say what they didn't find. They did not find evidence that gravity works differently than Einstein predicted. If gravity were behaving strangely (like in some "modified gravity" theories), the growth rate would have been different. Instead, the data says gravity is doing exactly what it's supposed to do.

They also explicitly ruled out using the full set of Tully-Fisher (spiral galaxy) velocity data without a filter. When they first looked at the spiral galaxies, the data showed a strange, extra-strong connection that didn't make sense. To be safe and honest, they cut out the spiral galaxies that were too far away (those with a redshift greater than 0.05) and only used the closer ones. They admit they don't fully understand why the distant ones were acting weird, but they decided to be conservative and ignore that part of the data to ensure their final answer was trustworthy.

How Sure Are They?

The team is confident in their numbers, but they are also realistic. They tested their method using 675 simulated universes (called "mocks") to make sure their math worked. In these simulations, their method worked perfectly, recovering the "true" growth rate every time.

However, they note that their current result isn't a "breakthrough" that changes physics. The error bars (the range of uncertainty) are still a bit wide—about 20% for their main measurement. They explain that this is because the DESI survey is still in its early stages (Data Release 1). They have a huge sample, but it's not the entire sky yet. They predict that when they analyze the full dataset in the future (Data Release 2), the error bars will shrink, and the measurement will become even sharper.

The Bottom Line

This paper is a massive step forward in mapping the local universe. By measuring how galaxies move and clump together, the team confirmed that our current understanding of gravity and the growth of cosmic structures is solid. They didn't find a crack in the theory of General Relativity; instead, they provided a very precise, albeit slightly fuzzy, confirmation that the universe is growing exactly as Einstein's equations say it should. It's a victory for the standard model, and a promise that even better measurements are on the way.

Technical Summary: The DESI DR1 Peculiar Velocity Survey: Growth Rate Measurements from Galaxy and Momentum Correlation Functions

Problem and Motivation
The paper addresses the need for robust tests of cosmological models of gravity, particularly in the context of current tensions in cosmology (e.g., dark energy evolution, the Hubble tension). While the local universe is insufficient for precise galaxy clustering measurements due to volume limitations, it serves as a powerful laboratory for testing gravitational physics through "peculiar velocities." These velocities, induced by the gravitational influence of large-scale structure, cause deviations from the Hubble flow. The authors aim to measure the normalised growth rate of structure, $f\sigma_8$ , by jointly analyzing the local peculiar velocity field and the galaxy density field. This approach complements traditional redshift-space distortion (RSD) analyses by probing momentum correlations, which trace the underlying matter power spectrum on large scales where modified gravity effects might be visible before screening mechanisms take effect.

Methodology
The study utilizes the first year of data (DR1) from the Dark Energy Spectroscopic Instrument (DESI) Peculiar Velocity (PV) survey and the Bright Galaxy Survey (BGS).

Datasets: The analysis combines a galaxy density sample from the DESI BGS (restricted to $z < 0.1$ and $M_r < -17.7$ to ensure constant number density) with peculiar velocity tracers. The velocity sample consists of 73,686 galaxies from the Fundamental Plane (FP) relation (early-type ellipticals) and 2,929 galaxies from the Tully-Fisher (TF) relation (late-type spirals). The TF sample was conservatively truncated at $z < 0.05$ due to an observed excess correlation at higher redshifts. The effective redshift of the combined sample is $z_{eff} = 0.07$ .
Statistical Framework: The authors measure five two-point correlation functions:
1. Momentum auto-correlations ( $\psi_1, \psi_2$ ).
2. Galaxy density auto-correlation multipoles (monopole $\xi^0_{gg}$ and quadrupole $\xi^2_{gg}$ ).
3. Galaxy-momentum cross-correlation dipole ( $\xi^1_{gu}$ ).
Modeling: Theoretical models for these statistics are constructed using 1-loop Eulerian perturbation theory to generate non-linear density and momentum power spectra, which are then transformed into configuration space. The models depend on five free parameters: the normalised growth rate ( $f\sigma_8$ ), linear bias ( $b_1\sigma_8$ ), second-order bias ( $b_2\sigma_8$ ), and two non-linear velocity dispersion terms ( $\sigma^2_{vT}, \sigma^2_{vS}$ ).
Estimators: The analysis employs optimal weighting schemes (Feldman-Kaiser-Peacock style) for both galaxy density and peculiar velocity (using log-distance ratios $\eta$ ) to balance sample variance and noise. A custom code, crosscorr, was developed to handle the specific geometric dependencies of momentum correlation estimators.
Validation: The methodology is validated using 675 mock catalogues generated from the AbacusSummit simulations, subsampled to match the DESI DR1 selection functions and noise characteristics. The covariance matrix is derived from these mocks, with a Hartlap correction applied to account for the finite number of realizations.

Key Contributions

Largest Sample to Date: This work presents the analysis of the largest catalogue of peculiar velocities assembled to date, containing over 76,000 velocity measurements and 415,000 galaxy redshifts.
Joint Analysis: It provides a comprehensive joint analysis of velocity and density fields using correlation functions, a method distinct from the power spectrum and maximum-likelihood field approaches also applied to the same DESI DR1 datasets in companion papers.
Methodological Rigor: The paper details the construction of non-linear correlation function models derived from perturbation theory and demonstrates their robustness through extensive mock testing, including sensitivity analyses on fitting ranges.
Consensus Determination: It contributes to a combined "consensus" growth rate measurement by integrating results from three distinct statistical methods (correlation functions, power spectra, and maximum-likelihood fields) applied to the same dataset.

Results

Growth Rate Measurement: The primary result from the correlation function analysis is a measurement of the normalised growth rate at $z=0.07$ :
$f\sigma_8(z=0.07) = 0.391^{+0.080}_{-0.081}$
This represents a 20.6% error.
Comparative Performance:
- Combining momentum and clustering statistics improved the error by 33.9% compared to clustering-only fits.
- Including the cross-correlation dipole further improved the error by 5.3% over the joint momentum-clustering fit.
- The result is consistent within $1\sigma$ with accompanying analyses of the same datasets using power spectrum ( $f\sigma_8 = 0.443^{+0.113}_{-0.070}$ ) and maximum-likelihood methods ( $f\sigma_8 = 0.482^{+0.049}_{-0.026}$ ).
Consensus Value: By combining the results from the three methods (accounting for correlations via AbacusSummit mocks), the authors derive a consensus determination:
$f\sigma_8(z=0.07) = 0.4497 \pm 0.0548$
This value is consistent with the Planck+ $\Lambda$ CDM prediction ( $f\sigma_8 \approx 0.446$ ).
Gravitational Growth Index: Jointly fitting this low-redshift consensus growth rate with the DESI DR1 full-shape clustering dataset yields a gravitational growth index $\gamma_L = 0.580^{+0.110}_{-0.110}$ , which is consistent with the General Relativity prediction of $\gamma \approx 0.55$ .

Significance and Claims
The paper claims that while the precision of the growth rate measurement from the correlation function method (20.6% error) is only marginally improved over previous studies (e.g., SDSS PV, 6dFGS), this is attributed to the incomplete sky coverage of the DESI DR1 dataset relative to the full survey footprint. The significance of this work lies in:

Demonstrating Scalability: Successfully applying these techniques to the largest peculiar velocity sample ever assembled, validating the pipeline for future, larger datasets.
Complementarity: Showing that peculiar velocity measurements provide competitive constraints on gravitational physics, with the consensus error (12.2%) already exceeding the precision of equivalent results from the full DR1 BGS redshift-space distortion studies.
Testing Gravity: Providing a measurement consistent with General Relativity and $\Lambda$ CDM, thereby supporting the standard cosmological model in the local universe while establishing a baseline for detecting potential deviations in future, more complete surveys (e.g., DESI DR2).

The authors remain modest regarding the current precision, noting that significant improvements are anticipated once the full DESI survey is complete and Data Release 2 is analyzed.

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