🔭 astrophysics

The DESI DR1 Peculiar Velocity Survey: growth rate measurements from the maximum likelihood fields method

Using the maximum likelihood fields method on a combined DESI DR1 dataset of over 415,000 redshifts and 76,000 peculiar velocities, the study measures a growth rate of structure consistent with the $\Lambda$ CDM cosmology and General Relativity.

Original authors: Y. Lai, C. Howlett, J. Aguilar, S. Ahlen, A. J. Amsellem, J. Bautista, S. BenZvi, D. Bianchi, C. Blake, D. Brooks, A. Carr, T. Claybaugh, T. M. Davis, A. de la Macorra, P. Doel, K. Douglass, S. Ferrar

Published 2026-04-13

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CC BY 4.0

Original authors: Y. Lai, C. Howlett, J. Aguilar, S. Ahlen, A. J. Amsellem, J. Bautista, S. BenZvi, D. Bianchi, C. Blake, D. Brooks, A. Carr, T. Claybaugh, T. M. Davis, A. de la Macorra, P. Doel, K. Douglass, S. Ferraro, A. Font-Ribera, J. E. Forero-Romero, E. Gaztañaga, G. Gutierrez, J. Guy, H. K. Herrera-Alcantar, D. Huterer, M. Ishak, R. Joyce, A. Kim, D. Kirkby, T. Kisner, A. Kremin, O. Lahav, C. Lamman, M. Landriau, L. Le Guillou, A. Leauthaud, M. E. Levi, M. Manera, P. Martini, A. Meisner, R. Miquel, J. Moustakas, A. Muñoz-Gutiérrez, S. Nadathur, W. J. Percival, C. Poppett, F. Prada, I. Pérez-Ràfols, F. Qin, C. Ross, G. Rossi, K. Said, E. Sanchez, D. Schlegel, M. Schubnell, H. Seo, J. Silber, D. Sprayberry, G. Tarlé, R. Turner, B. A. Weaver, P. Zarrouk, 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

Imagine the universe as a giant, invisible ocean. In this ocean, there are islands (galaxies) floating on the surface. According to the standard rules of physics (General Relativity), these islands should drift apart at a steady, predictable pace as the ocean expands. However, the islands also have their own little currents pushing them around—sometimes they get pulled closer by a nearby island's gravity, or pushed away by a storm. These extra movements are called peculiar velocities.

This paper is like a massive detective story where scientists used a new, super-powered telescope (DESI) to measure these tiny currents and figure out how fast the "islands" are actually clustering together. This clustering rate tells us if the rules of gravity are working exactly as we think they are.

Here is the breakdown of their adventure, explained simply:

1. The Mission: Measuring the "Drift"

For years, astronomers have tried to measure how fast the universe's structure is growing. Think of it like watching a crowd of people in a room. If they are just standing still, they are evenly spaced. But if they start running toward each other to form groups, the "clumping" rate tells you how strong the force pulling them together is.

The team used two main tools to measure this:

The Map of the Crowd (Galaxy Density): They counted how many galaxies are in different areas.
The Speedometers (Peculiar Velocities): They measured how fast galaxies are moving toward or away from us, beyond the normal expansion of the universe.

2. The New Toolkit: A Faster Computer Brain

The data they collected was enormous—over 400,000 galaxies and nearly 80,000 speed measurements. Trying to crunch these numbers with old computer methods would have taken weeks or even months.

To solve this, the scientists rewrote their software using a special "super-chip" language called JAX.

The Analogy: Imagine trying to solve a giant Sudoku puzzle. The old way was like doing it with a pencil and eraser, checking every number one by one. The new way is like having a robot that can check the whole board in a split second. This allowed them to run their complex calculations in hours instead of weeks, making their results much more precise.

3. The Two Types of "Speedometers"

To measure the galaxies' speeds, they used two different "rulers":

The Spiral Ruler (Tully-Fisher): Used for spiral galaxies (like our Milky Way).
The Elliptical Ruler (Fundamental Plane): Used for round, egg-shaped galaxies.

The Plot Twist: When they looked at the spiral galaxies far away (older in the universe), the numbers didn't match the round galaxies. It was like one group of speedometers saying "50 mph" and the other saying "100 mph" for the same car.

The Fix: The team realized the spiral galaxy ruler might have a hidden flaw when looking at distant objects. To be safe, they decided to ignore the spiral galaxy data beyond a certain distance and focus on the reliable round galaxies. This was a conservative choice to ensure their final answer wasn't wrong.

4. The Grid Game

Because there were so many galaxies, they couldn't measure every single one individually without the computer crashing. So, they divided the universe into a giant 3D grid (like a giant egg carton).

The Analogy: Instead of counting every single grain of sand on a beach, you count the sand in each square of a grid. This smoothed out the noise and made the math manageable. They found that using a grid size of about 20 million light-years was the "Goldilocks" zone—not too big to lose detail, not too small to crash the computer.

5. The Big Reveal: Gravity is Working (For Now)

After all the calculations, they found the growth rate of the universe's structure to be 0.450.

What does this mean? It matches the prediction made by the standard model of the universe (which includes Einstein's gravity and Dark Energy) almost perfectly.
The "Hubble Tension" Context: There is a famous disagreement in physics right now about how fast the universe is expanding. Some measurements say it's fast, others say it's slow. This study didn't solve that specific mystery, but it did confirm that gravity is behaving exactly as Einstein predicted on large scales. The "islands" are clustering together at the exact rate the standard rules say they should.

6. The Consensus

The team didn't just use one method. They had three different ways to measure the growth rate (like three different detectives solving the same case).

Detective A (This paper): Used the "Maximum Likelihood" method (fitting the whole map).
Detective B: Used "Velocity Correlations" (how speeds relate to each other).
Detective C: Used "Momentum Power Spectrum" (looking at the energy of the flow).

All three detectives agreed on the answer. When they combined their notes, the final result was very tight and precise.

The Bottom Line

This paper is a triumph of data science and teamwork. By using a massive new telescope, a super-fast computer algorithm, and a very careful approach to cleaning up bad data, the scientists confirmed that our current understanding of gravity is solid. The universe is growing and clumping together exactly as the "Standard Model" predicts, at least for now.

In one sentence: They built a super-fast computer model to measure how galaxies drift in the cosmic ocean, and found that the currents are flowing exactly as Einstein's laws of gravity predicted.

1. Problem Statement

The paper addresses the need for high-precision measurements of the linear growth rate of structure ( $f\sigma_8$ ) to test General Relativity (GR) and the standard $\Lambda$ CDM cosmological model.

Context: While the $\Lambda$ CDM model explains cosmic acceleration via a cosmological constant, tensions exist (e.g., the Hubble tension) and the nature of dark energy remains unclear. Modified gravity theories predict different growth rates compared to GR.
Challenge: Measuring $f\sigma_8$ requires combining galaxy density fields with peculiar velocities (deviations from Hubble flow). Previous analyses (e.g., SDSS) were limited by small sample sizes and computational constraints that forced approximations (like Taylor expansions of the likelihood) which could introduce systematics.
Specific Issue: The DESI DR1 Peculiar Velocity (PV) catalogue is the largest to date (~80,000 measurements), combining Tully-Fisher (spiral) and Fundamental Plane (elliptical) relations. However, initial tests revealed inconsistencies between the two samples at redshifts $z > 0.05$ , likely due to unknown systematics in the Tully-Fisher relation at higher redshifts.

2. Methodology

The authors employ the Maximum Likelihood Fields (MLF) method, which directly fits the correlation between the galaxy overdensity field ( $\delta_g$ ) and the log-distance ratio field ( $\eta$ ).

Data Processing

Catalogues:
- Peculiar Velocities: DESI DR1 Fundamental Plane (73,822 galaxies) and Tully-Fisher (6,806 galaxies) catalogues.
- Density Field: DESI DR1 Bright Galaxy Sample (BGS) with 415,523 galaxies ( $z < 0.1$ ).
Quality Cuts:
- Redshift Cut: Tully-Fisher galaxies with $z > 0.05$ are removed due to inconsistencies with the Fundamental Plane sample.
- Outlier Removal: Log-distance ratios deviating by $>4\sigma$ from the median are removed.
- Final Sample: 76,616 peculiar velocity measurements and 415,523 density measurements.
Gridding: To handle the computational cost of a $\sim500,000 \times 500,000$ covariance matrix, data is binned into $20h^{-1}\text{Mpc}$ grid cells. This reduces dimensionality and smooths non-linearities.

Theoretical Modelling

Likelihood Function: Assumes a Gaussian likelihood for the data vector $S = (\delta_g, \eta)$ .
Covariance Matrix:
- Derived analytically using Standard Perturbation Theory (SPT) (chosen for consistency with companion papers, though Appendix A shows SPT and RPT yield similar $f\sigma_8$ constraints).
- Includes corrections for Redshift Space Distortions (RSD) (Finger-of-God effect) via damping terms ( $\sigma_g, \sigma_u$ ).
- Accounts for shot noise and gridding effects (modifying the power spectrum with a gridding kernel $\Gamma(k)$ ).
- Includes a zero-point correction marginalization to account for calibration uncertainties.
Computational Efficiency:
- JAX Implementation: The code was rewritten in Python using JAX to utilize Just-In-Time (JIT) compilation and XLA accelerators.
- Cholesky Decomposition: Used to speed up the inversion of the covariance matrix.
- Result: Likelihood evaluation time dropped from hours/days to ~1 second per iteration, allowing for exact likelihood calculations without Taylor expansion approximations.
- MCMC: Uses Adaptive Sampling Metropolis-Hastings (Numpyro) for convergence.

Mock Validation

675 mock catalogues based on AbacusSummit simulations were used to test the pipeline.
Key Finding: The pipeline returns unbiased $f\sigma_8$ constraints.
Uncertainty Inflation: The mock standard deviation of $f\sigma_8$ was found to be larger than the mean statistical uncertainty estimated by the Fisher matrix. To account for this sample variance underestimation, the final error bars were inflated by a factor of $\sim1.64$ .

3. Key Contributions

First Large-Scale MLF Analysis: This is the first application of the maximum likelihood fields method to the largest peculiar velocity catalogue to date (DESI DR1), significantly surpassing the SDSS sample size.
Computational Breakthrough: By rewriting the algorithm in JAX, the authors eliminated the need for second-order Taylor expansion approximations of the likelihood, thereby improving the accuracy of the constraints.
Systematic Identification: Identified and addressed inconsistencies in the Tully-Fisher relation at $z > 0.05$ , leading to a conservative redshift cut to ensure robust results.
Multi-Tracer Consistency: Demonstrated that three independent DESI analysis pipelines (Maximum Likelihood Fields, Momentum Power Spectrum, and Velocity Correlation Function) yield consistent growth rate measurements.

4. Results

Individual Constraint: Using the MLF method on the combined BGS + PV data (with $z_{\text{eff}} = 0.07$ $z_{eff} = 0.07$ ):
$f\sigma_8 = 0.483^{+0.080}_{-0.043}(\text{stat}) \pm 0.018(\text{sys})$
- The statistical uncertainty is 13% (after inflation).
- The result is consistent with the GR prediction from Planck $\Lambda$ CDM ( $f\sigma_8 = 0.449$ ) within $1\sigma$ .
Consensus Constraint: Combining the MLF result with the two companion papers (Momentum Power Spectrum and Velocity Correlation Function) using appropriate correlations:
$f\sigma_8(z_{\text{eff}} = 0.07) = 0.450 \pm 0.055$
- This is consistent with the Planck $\Lambda$ CDM prediction within $1\sigma$ .
Growth Index ( $\gamma$ ): Combining the low-redshift DESI PV constraint with high-redshift DESI ShapeFit measurements:
$\gamma = 0.58 \pm 0.11$
- This is consistent with the GR prediction ( $\gamma \approx 0.55$ ).
Precision: The MLF constraint is approximately 30% tighter than previous constraints from the SDSS peculiar velocity catalogue.

5. Significance

Validation of GR: The results provide strong support for General Relativity on cosmological scales, showing no significant deviation in the growth rate of structure from the $\Lambda$ CDM prediction.
Methodological Advancement: The successful application of JAX to large-scale structure analysis sets a new standard for handling massive datasets in cosmology, enabling exact likelihood evaluations that were previously computationally prohibitive.
Future Prospects: The paper highlights that while current constraints are limited by systematic uncertainties (specifically the fixed damping parameter $\sigma_u$ ), future data releases (DESI DR2+) will increase sample sizes. The authors propose using lossless data compression (e.g., MOPED) to handle the memory requirements of varying $\sigma_u$ as a free parameter in future analyses, which will further tighten constraints on modified gravity theories.