🔭 astrophysics

Inference of matter power spectrum at z=0 using DESI DR1 Full-Shape data

This study utilizes DESI DR1 galaxy clustering data combined with CMB observations and Effective Field Theory modeling to reconstruct the present-day matter power spectrum, finding that both the standard $\Lambda$ CDM and the dynamical $w_0w_a$ CDM cosmological models provide consistent fits to the data.

Original authors: R. Cereskaite, E. Mueller, C. Howlett, Tamara M. Davis, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, F. J. Castander, T. Claybaugh, A. Cuceu, A. de la Macorra, S. Ferraro, A. Font-Ribera, J. E. Forero

Published 2026-05-21

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: R. Cereskaite, E. Mueller, C. Howlett, Tamara M. Davis, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, F. J. Castander, T. Claybaugh, A. Cuceu, A. de la Macorra, S. Ferraro, A. Font-Ribera, J. E. Forero-Romero, E. Gaztanaga, G. Gutierrez, C. Hahn, K. Honscheid, D. Huterer, M. Ishak, R. Joyce, S. Juneau, D. Kirkby, A. Kremin, O. Lahav, A. Lambert, M. Landriau, L. Le Guillou, M. Manera, A. Meisner, R. Miquel, J. Moustakas, S. Nadathur, J. A. Newman, N. Palanque-Delabrouille, W. J. Percival, F. Prada, I. Perez-Rafols, G. Rossi, E. Sanchez, D. Schlegel, 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

The Big Picture: Reconstructing a Faded Photograph

Imagine you have a very old, slightly blurry photograph of a city taken from a high tower. You want to know exactly what that city looks like right now, today. But you can't just walk there and take a new picture; you only have that old photo.

To figure out the present-day city, you have to do two things:

Understand the camera: You need to know how the old camera distorted the image (the "lens" of the universe).
Run a simulation: You use a computer model to "undo" the blur and the aging process, predicting what the city looks like today based on the rules of how cities grow and change.

This paper is about doing exactly that for the Universe. The authors used data from the DESI (Dark Energy Spectroscopic Instrument) survey, which is like a massive telescope taking pictures of millions of galaxies. They wanted to reconstruct the "map" of the universe as it exists today ( $z=0$ ), even though the galaxies they observed are far away and their light has been traveling for billions of years.

The Tools: Two Different Maps

The researchers combined two very different types of cosmic data to build this map:

The Baby Picture (CMB): This is the Cosmic Microwave Background. It's the "afterglow" of the Big Bang, a snapshot of the universe when it was a baby (very hot and dense). It tells us about the very large scales of the universe.
The Teenage Photo (DESI): This is the new data from DESI, which looks at galaxies in the "teenage" years of the universe (closer to us in time). It shows how matter is clumped together in the middle scales.

The challenge is that these two "photos" were taken at different times and with different "cameras." The authors had to translate both into a common language (a 3D map of matter density) to see if they tell the same story.

The New Trick: Better Glasses (EFT)

In the past, scientists used a simple pair of glasses to look at the galaxy data. These glasses worked okay, but they got blurry when looking at the smaller, more complex details (like how galaxies move and cluster tightly together).

In this paper, the authors upgraded to High-Definition Glasses called Effective Field Theory (EFT).

The Analogy: Imagine trying to predict traffic flow. A simple model might just say "cars move forward." But a better model (EFT) accounts for traffic jams, sudden stops, and lane changes.
The Result: By using EFT, the authors could model the "traffic" of galaxies much more accurately. This allowed them to extract a cleaner, more precise map of the underlying matter, removing the "noise" caused by complex galaxy movements.

The Experiment: Testing the Rules of the Game

The universe is currently expanding, and scientists are trying to figure out why. There are two main theories (rulesets) they tested:

The Standard Rulebook ( $\Lambda$ CDM): This is the current "best guess." It says the universe is made of normal matter, dark matter, and a constant form of energy (Dark Energy) that pushes everything apart at a steady rate.
The Flexible Rulebook ( $w_0w_a$ CDM): This is a newer theory that suggests Dark Energy might be changing its strength over time, like a rubber band that gets tighter or looser as the universe expands.

The authors took their reconstructed map of the universe and asked: "Which rulebook fits this map better?"

The Findings: A Tie

After running the numbers and comparing their reconstructed map against both rulebooks, the results were:

Both fit well: The map of the universe they built from the DESI data looks consistent with both the Standard Rulebook and the Flexible Rulebook.
No clear winner: While some other studies using different data suggested the Flexible Rulebook might be better, this specific study using DESI's "Full-Shape" data (which looks at the whole shape of the galaxy distribution, not just specific peaks) found no strong evidence to reject the Standard Rulebook.
Consistency: The "Baby Picture" (CMB) and the "Teenage Photo" (DESI) agree with each other when viewed through the Standard Rulebook.

The Conclusion

Think of this paper as a rigorous quality control check. The authors took the best new data we have (DESI), used the most advanced modeling tools available (EFT), and tried to see if the universe is behaving exactly as the standard model predicts or if it's doing something weird (changing Dark Energy).

The verdict? The universe is behaving exactly as the standard model predicts, at least based on this specific dataset. The "Flexible Rulebook" isn't wrong, but this data doesn't prove it's necessary either. The two theories are currently indistinguishable using this specific method, meaning the standard model remains a very strong contender for describing our universe.

Technical Summary: Inference of the Linear Matter Power Spectrum at $z=0$ using DESI DR1 Full-Shape Data

Problem Statement
While the standard $\Lambda$ CDM model has been highly successful, recent analyses combining Dark Energy Spectroscopic Instrument (DESI) Year 1 (DR1) data with other probes (CMB, Supernovae) suggest a potential deviation in the expansion history, favoring a time-varying dark energy equation of state ( $w_0w_a$ CDM) over the standard cosmological constant ( $w_0=-1, w_a=0$ ). However, individual datasets often provide limited constraints on dark energy. Furthermore, while various cosmological probes (CMB, galaxy clustering, weak lensing) trace the underlying matter field, they do not directly measure the matter power spectrum ( $P_m$ ) due to complex astrophysical processes like galaxy bias and redshift-space distortions (RSD). To rigorously test the consistency of cosmological models across cosmic time, it is necessary to reconstruct the underlying linear matter power spectrum at the present epoch ( $z=0$ ) from high-redshift observations and compare it against theoretical predictions.

Methodology
This study reconstructs the 3D linear matter power spectrum at $z=0$ by combining Cosmic Microwave Background (CMB) data from Planck 2018 with Full-Shape galaxy clustering data from DESI DR1. The analysis employs a two-pronged approach:

CMB Reconstruction: Following the methodology of [22], the authors extrapolate high-redshift CMB angular power spectrum data ( $C_\ell$ ) to low redshift. This involves a convolution process where CMB multipoles are weighted by transfer functions to map angular scales ( $\ell$ ) to Fourier wavenumbers ( $k$ ) at $z=0$ . The recovered power spectrum is derived by taking the ratio of observed data to a theoretical $\Lambda$ CDM model, scaled by transfer functions.
Galaxy Clustering Reconstruction: The analysis utilizes the "Full-Shape" data (encompassing both BAO positions and the spectral shape) from five DESI tracers: Bright Galaxy Survey (BGS), Luminous Red Galaxies (LRG), Emission Line Galaxies (ELG), and Quasars (QSO). Unlike previous works that relied on simple linear bias models, this study implements the Effective Field Theory of Large Scale Structure (EFTofLSS) using the velocileptors code. This framework models the galaxy power spectrum ( $P_g$ $P_{g}$ ) by incorporating one-loop corrections and counterterms ( $\alpha_n, SN_n$ $α_{n}, S N_{n}$ ) to account for small-scale non-linear dynamics and stochastic effects.
- Kernel Extraction: A key methodological challenge is extracting the representative wavenumbers ( $k_{m,i}$ ) for the reconstructed power spectrum. While CMB requires complex window functions, the authors propose a simplified approach for galaxy data using a Kaiser-model approximation to define "Galaxy Kernels." These kernels allow the separation of the matter power spectrum from EFT counterterms, enabling the calculation of $k_{m,i}$ values (median scales) and their associated uncertainties.
- Cosmological Scenarios: The analysis is performed under two assumptions: the standard $\Lambda$ CDM model and the time-varying $w_0w_a$ CDM model. For the latter, cosmological parameters are fixed to marginalized mean values derived from a Bayesian analysis of DESI DR1 combined with external CMB and SN Ia data.

Key Contributions

Application of EFT to Power Spectrum Reconstruction: The paper advances the state-of-the-art by applying EFT modeling (specifically the velocileptors framework) to the reconstruction of the matter power spectrum, rather than just fitting galaxy clustering parameters. This provides a more robust handling of small-scale effects and RSD compared to previous linear bias approaches.
Unified $z=0$ Inference: The study successfully casts distinct datasets (CMB at $z \sim 1100$ and DESI galaxies at $0.1 < z < 1.1$ ) into a common $k$ -space representation at $z=0$ . This allows for a direct visual and statistical comparison of the matter power spectrum across different redshift regimes and probes.
Methodological Refinement: The authors introduce a simplified, Kaiser-based approximation for determining $k_{m,i}$ and error bars for galaxy clustering data, validating this approach against DESI mock catalogs to ensure robustness in the quasi-linear regime.

Results

Consistency with $\Lambda$ CDM: The reconstructed linear matter power spectrum from DESI DR1 Full-Shape data, when combined with Planck CMB data, is consistent with the $\Lambda$ CDM model. Goodness-of-fit tests ( $\chi^2$ ) generally indicate acceptable agreement, particularly when accounting for uncertainties in the $k$ -binning (horizontal error bars).
Consistency with $w_0w_a$ CDM: When the analysis is repeated assuming a $w_0w_a$ CDM background (with parameters favoring evolving dark energy), the reconstructed power spectrum remains consistent with the data. The nuisance parameters in the EFT model absorb much of the cosmological differences between the two models, resulting in similar fits.
Residual Trends: Visual inspection of residuals (Figure 5) reveals a slight upward trend in the $\Lambda$ CDM case that is less pronounced in the $w_0w_a$ CDM case. However, these visual differences are not strongly reflected in the $\chi^2$ statistics or $p$ -values, suggesting that current data precision or modeling sensitivity is insufficient to definitively distinguish between the two models based solely on this reconstruction method.
Tracer Performance: Individual tracers (BGS, LRGs, ELG2, QSO) show varying degrees of fit quality, with some (like LRG1 and LRG2) showing larger $\chi^2$ values in the quadrupole moment. Combining monopole and quadrupole moments generally improves the fit statistics.

Significance and Claims
The authors claim that this work provides a transparent and effective compatibility test for cosmological models by directly tracing the underlying matter power spectrum across different observations, scales, and redshifts. The primary significance lies in demonstrating that:

DESI DR1 Full-Shape data is consistent with both $\Lambda$ CDM and $w_0w_a$ CDM models when analyzed through this reconstruction lens.
The EFT-based approach improves the modeling of the galaxy power spectrum, offering a more robust consistency check than previous methods.
While the method is not model-independent (relying on assumptions like Kaiser modeling and a fixed background cosmology), it serves as a valuable qualitative consistency check that complements standard Bayesian parameter inference.

The paper concludes that while no strong preference for either cosmology is found in the current DESI DR1 data using this specific metric, the approach offers a flexible framework for future high-precision cosmology, particularly as more data (e.g., Ly- $\alpha$ forest) becomes available to further test the expansion history.