🔭 astrophysics

The DESI DR1 peculiar velocity survey: growth rate measurements from the galaxy power spectrum

This paper presents a generalized cross-power spectrum model applied to DESI DR1 data to measure the growth rate of structure, yielding a consensus value of $f\sigma_8=0.450$ at $z_{\rm eff}=0.07$ that is consistent with predictions from the $\Lambda$ CDM model and General Relativity.

Original authors: F. Qin, C. Blake, C. Howlett, R. J. Turner, K. Lodha, J. Bautista, Y. Lai, A. J. Amsellem, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, S. BenZvi, A. Carr, E. Chaussidon, T. Claybaugh, A. Cuceu, A. de

Published 2026-02-17

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CC BY 4.0

Original authors: F. Qin, C. Blake, C. Howlett, R. J. Turner, K. Lodha, J. Bautista, Y. Lai, A. J. Amsellem, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, S. BenZvi, A. Carr, E. Chaussidon, T. Claybaugh, A. Cuceu, A. de la Macorra, K. Douglass, P. Doel, 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, D. Huterer, M. Ishak, R. Joyce, A. G. Kim, D. Kirkby, T. Kisner, A. Kremin, O. Lahav, C. Lamman, M. Landriau, L. Le Guillou, 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. Perez-Rafols, C. Ross, G. Rossi, E. Sanchez, D. Schlegel, K. Said, M. Schubnell, H. Seo, J. Silber, D. Sprayberry, G. Tarle, 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, galaxies aren't just floating aimlessly; they are swimming. Most of the time, they are drifting along with the current of the expanding universe (like a leaf floating downstream). But sometimes, they get pulled off course by the gravity of nearby "whirlpools" made of dark matter. These extra movements are called peculiar velocities.

This paper is like a team of cosmic detectives trying to figure out how fast these whirlpools are growing and how strong the gravity pulling the galaxies is. They use a new, high-tech method to measure the "growth rate" of the universe's structure.

Here is a breakdown of their work using simple analogies:

1. The Two Types of Data: The Map and the Wind

To solve the mystery, the team used two different datasets from the DESI (Dark Energy Spectroscopic Instrument) telescope, which is like a massive camera taking pictures of millions of galaxies.

The "Map" (Density Field): Think of this as a photo of where all the galaxies are standing. It tells us the location of the crowd. This came from the "Bright Galaxy Survey" (BGS).
The "Wind" (Momentum Field): This is trickier. It measures how fast the galaxies are moving toward or away from us due to gravity, not just the expansion of the universe. It's like measuring the wind speed at different points in the ocean. This came from the "Peculiar Velocity Survey" (DESI-PV).

The Innovation: In the past, scientists usually tried to get both the map and the wind from the same group of galaxies. This paper is special because they combined two different groups of galaxies (one for the map, one for the wind) to get a clearer picture. It's like trying to understand a storm by looking at a map of the clouds from one satellite and wind speed data from a different satellite, then stitching them together perfectly.

2. The Challenge: The "Window" Effect

Imagine you are trying to measure the sound of an orchestra, but you are listening through a small, oddly shaped window in a wall. The shape of the window distorts the sound, making some notes louder and others quieter.

In astronomy, the "window" is the shape of the sky area the telescope can see. It's not a perfect square; it's a weird shape with holes. When scientists measure the "power spectrum" (a fancy way of saying "how much structure exists at different sizes"), this window distorts the results.

The authors built a complex mathematical "noise-canceling headphone" (called a window function convolution) to subtract the distortion caused by the telescope's view, allowing them to hear the true "music" of the universe.

3. The Method: Listening to the Rhythm

Instead of just looking at the galaxies, the team analyzed the Power Spectrum.

The Analogy: Imagine the galaxies are dancers on a floor. The "Power Spectrum" is like analyzing the rhythm of their dance. Are they dancing in tight, small groups (small scales)? Or are they moving in huge, sweeping waves across the room (large scales)?
The Growth Rate ( $f\sigma_8$ ): This is the specific number they wanted to find. It tells us how fast the "dancers" are clustering together over time. If gravity is strong, they cluster fast. If gravity is weak (or dark energy is pushing them apart), they cluster slowly.

4. The Hiccup: The "Squeaky Wheel"

The team ran into a problem with one specific type of galaxy (the "Fundamental Plane" or FP galaxies).

The Analogy: Imagine you are trying to measure the speed of cars on a highway, but the speedometers on the red cars are slightly broken and always read too high. If you include those red cars, your average speed calculation will be wrong.
The Fix: They discovered that the FP galaxies had a systematic error in their speed measurements, especially at certain distances. To get an accurate answer, they had to ignore the "broken speedometers" and only use the reliable data from the closer galaxies. This made their final calculation a bit more conservative but much more trustworthy.

5. The Results: Does Einstein Still Win?

After crunching the numbers, they found:

The Growth Rate: They measured how fast structures are growing and found it to be 0.440 (with a small margin of error).
The Verdict: This number matches the predictions made by General Relativity (Einstein's theory of gravity) and the standard model of the universe (Lambda-CDM) almost perfectly.

What does this mean?
It means that, so far, our understanding of gravity and how the universe grows is correct. The "whirlpools" of dark matter are pulling galaxies together exactly as Einstein predicted they should.

6. The Big Picture

The authors also combined their results with other studies (using different math methods on the same data) to get a "consensus" value. This combined result is even more precise.

In summary:
This paper is a triumph of data engineering and mathematical modeling. The team successfully built a new tool to measure the "heartbeat" of the universe by combining two different galaxy surveys. They corrected for the distortions of their telescope and the errors in their data, confirming that the universe is growing exactly as our current best theories say it should. They have also released their "code" (the mathematical tools they used) to the public, so other scientists can use it to solve even bigger cosmic mysteries in the future.

1. Problem Statement

The evolution of large-scale structures in the Universe encodes critical cosmological information, particularly regarding the nature of dark energy and the validity of General Relativity (GR). A primary observable for testing these theories is the growth rate of structure, parameterized as $f\sigma_8$ .

While previous studies have utilized the auto-power spectrum of galaxy density or the cross-correlation of density and velocity fields, a significant challenge remains in analyzing scenarios where the density field and the momentum (velocity) field are derived from distinct galaxy survey catalogs. These catalogs often possess different survey geometries, selection functions, and sample characteristics. Furthermore, systematic biases in peculiar velocity measurements (specifically in Fundamental Plane data) can distort power spectrum estimates at small scales, complicating the extraction of precise cosmological parameters.

2. Methodology

Data Sources

The study utilizes DESI Data Release 1 (DR1):

Density Field: Derived from the Bright Galaxy Survey (BGS), containing ~415,000 galaxies ( $0.01 < z < 0.1$ ).
Momentum Field: Derived from the Peculiar Velocity Survey (DESI-PV), a combination of:
- Tully-Fisher (TF) sample: ~6,800 late-type galaxies.
- Fundamental Plane (FP) sample: ~73,800 early-type galaxies.
Mocks: 675 mock catalogs generated from the AbacusSummit simulation, designed to replicate the selection functions and geometries of both BGS and DESI-PV.

Theoretical Framework & Estimators

Generalized Cross-Power Spectrum: The authors generalize the cross-power spectrum model to accommodate cases where density and momentum fields come from different surveys. This involves deriving new loop terms ( $P_{mn}$ ) for the one-loop perturbation theory models that account for distinct bias parameters ( $b^\delta, b^p$ ) and window functions for each field.
Field Definitions:
- Density contrast: $\delta(\mathbf{r}) = (\rho - \bar{\rho})/\bar{\rho}$ .
- Momentum field: $p(\mathbf{r}) = [1+\delta(\mathbf{r})]v(\mathbf{r})$ .
Multipole Estimators: The redshift-space power spectrum is decomposed into Legendre multipoles. The study focuses on:
- Auto-density: Monopole ( $P^\delta_0$ ) and Quadrupole ( $P^\delta_2$ ).
- Auto-momentum: Monopole ( $P^p_0$ ).
- Cross-power: Dipole ( $P^{\delta p}_1$ ).
Window Function Convolution: To account for survey geometry and mask effects, the theoretical models are convolved with a window function matrix derived from random catalogs. The authors include multipoles up to $\ell_{max}=4$ in the convolution to ensure accuracy, even if only lower orders are fitted.
Fitting Strategy:
- A likelihood function based on a modified $t$ -distribution (Sellentin & Heavens 2016) is used to handle the uncertainty in the covariance matrix derived from a finite number of mocks (Hartlap effect).
- Parameters: The fit constrains 5 key parameters: $f\sigma_8$ , linear bias $b_1\sigma_8$ , second-order bias $b_2\sigma_8$ , and velocity dispersions $\sigma_{vT}$ and $\sigma_{vS}$ .
- Scale Cuts: A conservative cutoff of $k^p_{max} = 0.1 \, h \, \text{Mpc}^{-1}$ is applied to the momentum power spectrum to avoid systematic biases, while $k_{max} = 0.3 \, h \, \text{Mpc}^{-1}$ is used for density and cross-spectra.

3. Key Contributions

Generalized Formalism: The paper extends the cross-power spectrum methodology to handle heterogeneous survey catalogs (different density and momentum tracers), a necessary step for modern surveys like DESI where different galaxy populations are used for different field reconstructions.
Correction of Loop Terms: The authors identify and correct minor inaccuracies in the derivation of cross-power spectrum loop terms found in previous literature (Okumura et al. 2014; Qin et al. 2025), providing the corrected analytical expressions for $P_{mn}$ .
Systematic Bias Identification: The study rigorously identifies a systematic bias in the Fundamental Plane (FP) peculiar velocity data, where measured momentum power spectra are artificially elevated at $k > 0.1 \, h \, \text{Mpc}^{-1}$ . This leads to a robust strategy of restricting the momentum analysis to larger scales.
Code Release: The authors release public Python code for power spectrum estimators, theoretical models, and window function convolution, facilitating reproducibility and future research.

4. Results

Validation with Mocks

The methodology was tested on 675 mock sets.
The fitting framework successfully recovered the fiducial growth rate ( $f\sigma_8 = 0.466$ ) with high accuracy: $f\sigma_8 = 0.468^{+0.061}_{-0.043}$ at effective redshift $z_{eff}=0.2$ .
The models demonstrated robustness up to non-linear scales of $k_{max} = 0.3 \, h \, \text{Mpc}^{-1}$ for density/cross-spectra.

DESI DR1 Measurements

Growth Rate: At effective redshift $z_{eff} = 0.07$ , the joint fit yields:
$f\sigma_8 = 0.440^{+0.080}_{-0.096}$
Consensus Value: By synthesizing results from this paper (Power Spectrum), Turner et al. (2025) (Correlation Functions), and Lai et al. (2025) (Maximum Likelihood), a consensus value is derived:
$f\sigma_8(z_{eff}=0.07) = 0.450 \pm 0.055$
Cosmological Parameters: Using the consensus $f\sigma_8$ $f σ_{8}$ combined with DESI DR1 ShapeFit and BAO data, the authors constrain:
- Growth index: $\gamma = 0.580^{+0.110}_{-0.110}$
- Matter density: $\Omega_m = 0.301 \pm 0.011$
- Fluctuation amplitude: $\sigma_8 = 0.834^{+0.032}_{-0.032}$

5. Significance

Consistency with Standard Model: The measured growth rate and growth index are consistent with the predictions of the $\Lambda$ CDM model and General Relativity (which predicts $\gamma \approx 0.55$ ).
Precision Improvement: The inclusion of Peculiar Velocity (PV) data significantly tightens constraints on cosmological parameters. Compared to ShapeFit+BAO alone, the addition of PV data reduced errors on $\gamma$ , $\Omega_m$ , and $\sigma_8$ by approximately 32%, 33%, and 20%, respectively.
Tension Analysis: While individual measurements align with GR, a joint analysis of all available $f\sigma_8$ data points suggests a slight preference for a higher growth index ( $\gamma \approx 0.63$ ), hinting at potentially weaker gravity, though this is not statistically significant enough to rule out GR given current covariances.
Future Outlook: This work establishes the framework for analyzing DESI Data Release 2 (DR2), which will offer a more homogeneous and extensive peculiar velocity sample, potentially allowing for measurements at smaller scales ( $k > 0.1 \, h \, \text{Mpc}^{-1}$ ) and tighter constraints on modified gravity.