🔭 astrophysics

FolpsD: combining EFT and phenomenological approaches for joint power spectrum and bispectrum analyses

The paper introduces FolpsD, a public code that combines EFT-based power spectrum and tree-level bispectrum models with line-of-sight damping to significantly tighten cosmological constraints on parameters like $A_s$ , $\omega_{cdm}$ , and dark energy equation of state when applied to DESI DR2 mocks, while highlighting the method's sensitivity to tracer signal-to-noise ratios.

Original authors: P. Bansal, A. Aviles, H. E. Noriega, C. Guandalin, I. Garzon, G. Niz, M. S. Wang, U. Andrade, F. Beutler, A. de Mattia, D. Gonzalez, J. Hou, D. Huterer, E. Paillas, M. Pellejero Ibanez, J. Aguilar, S.

Published 2026-04-13

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: P. Bansal, A. Aviles, H. E. Noriega, C. Guandalin, I. Garzon, G. Niz, M. S. Wang, U. Andrade, F. Beutler, A. de Mattia, D. Gonzalez, J. Hou, D. Huterer, E. Paillas, M. Pellejero Ibanez, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, T. Claybaugh, A. Cuceu, A. de la Macorra, B. Dey, P. Doel, S. Ferraro, A. Font-Ribera, J. E. Forero-Romero, E. Gaztañaga, S. Gontcho A Gontcho, G. Gutierrez, C. Hahn, H. K. Herrera-Alcantar, K. Honscheid, C. Howlett, M. Ishak, R. Joyce, S. Juneau, D. Kirkby, A. Kremin, M. Landriau, L. Le Guillou, M. Manera, A. Meisner, R. Miquel, S. Nadathur, W. J. Percival, F. Prada, I. Pérez-Ràfols, G. Rossi, L. Samushia, E. Sanchez, D. Schlegel, M. Schubnell, H. Seo, J. Silber, G. Tarlé, B. A. Weaver, P. Zarrouk, R. Zhou

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, cosmic ocean. For decades, astronomers have tried to understand how this ocean formed by looking at the "waves" of galaxies floating on its surface. These waves aren't random; they hold a secret code that tells us about the universe's history, its ingredients (like dark matter and dark energy), and how it is expanding.

This paper introduces a new, smarter way to read that code. The authors, part of the DESI collaboration, have developed a tool called FolpsD that combines two different ways of listening to the universe's song.

Here is the breakdown of their work using simple analogies:

1. The Two Songs: The Power Spectrum and the Bispectrum

To understand the universe, scientists usually listen to two types of "music":

The Power Spectrum (The Soloist): This is like listening to a single instrument playing a melody. It tells you how loud the waves are at different sizes. It's great for seeing the big picture, but it misses the complex interactions between the notes.
The Bispectrum (The Harmony): This is like listening to how three instruments play together. In the universe, galaxies don't just float alone; they cluster in triangles. The bispectrum measures these triangular patterns. It's much harder to hear, but it reveals hidden details about how the "notes" (galaxies) influence each other.

The Problem: The "Power Spectrum" soloist is easy to hear, but it gets noisy and distorted on small scales (like trying to hear a whisper in a storm). The "Bispectrum" harmony is rich in information but very faint and hard to measure.

2. The New Tool: FolpsD (The Smart Mixer)

The authors created FolpsD, a new software that acts like a high-tech audio mixer. It does two main things:

It turns up the volume on the "Soloist" (Power Spectrum):
Usually, scientists stop listening to the Power Spectrum when the waves get too small and messy because their math breaks down. FolpsD adds a "damping factor" (think of it as a noise-canceling headphone or a smooth filter). This allows them to listen to the music at much smaller, more detailed scales without getting confused by the noise.
- Analogy: Imagine trying to read a book in the rain. The standard method stops reading when the pages get wet. FolpsD puts a plastic cover over the book, allowing you to keep reading even when the rain is heavy.
It brings in the "Harmony" (Bispectrum):
FolpsD doesn't just listen to the solo; it actively listens to the triangular harmony of the galaxies. By combining the solo and the harmony, the tool gets a much clearer picture of the universe's structure.

3. The Results: A Sharper Picture

When the team tested FolpsD on simulated data (like a "flight simulator" for the universe), they found:

Better Precision: By listening to both the solo and the harmony, and by using the "noise-canceling" filter, they could measure the universe's properties (like how much dark matter exists) about 30% more precisely than before.
Breaking the Fog: Often, different theories look the same because the data is blurry. This new method clears the fog, helping scientists distinguish between different cosmic models.

4. The Catch: When the Filter Backfires

The paper also warns about a limitation. The "noise-canceling" filter works great when the signal is strong (like the Luminous Red Galaxies). However, for fainter, noisier objects (like Quasars), the filter can sometimes get confused.

Analogy: If you are in a quiet room, noise-canceling headphones work perfectly. But if you are in a chaotic, loud party, the headphones might try to cancel out the music you actually want to hear, making you think the music is different than it really is.
The Lesson: For very faint signals, the team found that the "filter" could accidentally hide the truth, leading to slightly wrong answers. They recommend being careful when using this tool on very noisy data.

5. The Big Discovery: Dark Energy Might Be Changing

The most exciting part of the paper is what they found when they applied this tool to real data from the DESI telescope (DESI DR1).

They tested a model where Dark Energy (the force pushing the universe apart) is constant versus a model where it changes over time.
Using FolpsD, they found a hint that Dark Energy might not be constant. The data suggests it might be changing, with a statistical significance of just over 1 standard deviation (a "maybe" in science terms, but a very promising hint).
Analogy: Imagine you are watching a car drive away. Standard models say the car is slowing down at a steady rate. FolpsD suggests the car might actually be pressing the gas pedal harder as it goes. It's a small hint, but it could change our understanding of the universe's fate.

Summary

FolpsD is a new, powerful tool that combines two ways of measuring the universe and uses a clever filter to see deeper into the cosmic noise. It allows scientists to measure the universe's ingredients with much higher precision. While it has some limitations with very faint signals, it has already provided the strongest hint yet that the mysterious force driving the universe's expansion (Dark Energy) might be changing over time.

1. Problem Statement

Extracting cosmological information from galaxy clustering data (specifically from the Dark Energy Spectroscopic Instrument, DESI) requires accurate theoretical modeling across a wide range of scales.

The Challenge: Standard Effective Field Theory (EFT) of Large Scale Structure (LSS) is robust on large, linear scales but becomes limited on mildly nonlinear scales due to the breakdown of perturbation theory and redshift-space distortions (RSD), specifically the "Finger-of-God" (FoG) effect.
Current Limitations: Conservative scale cuts (typically $k_{max} \approx 0.2 \, h\text{Mpc}^{-1}$ ) are often applied to avoid modeling systematics, discarding valuable small-scale information. Conversely, purely phenomenological damping models (like TNS) can extend the scale range but may violate fundamental symmetry constraints (Galilean invariance, momentum conservation) or introduce degeneracies with cosmological parameters.
Goal: The authors aim to develop a unified framework that combines the systematic rigor of EFT with phenomenological damping to extend the valid scale range for both the power spectrum ( $P(k)$ ) and the bispectrum ( $B(k)$ ), thereby improving constraints on cosmological parameters and galaxy bias.

2. Methodology: The FolpsD Framework

The authors extend the existing Folps (Fast Optimized Large-scale structure Perturbation Solver) code to create FolpsD. The methodology involves three key theoretical components:

A. Line-of-Sight (LoS) Damping Factor

To model the suppression of power on small scales due to random galaxy motions (FoG), the authors introduce a phenomenological damping factor, $D(x^2)$ , applied to the power spectrum and bispectrum.

Formulation: The damping factor is chosen to be Lorentzian: $D(x^2) = (1 + x^2)^{-1}$ , where $x = X_p f \sigma_v k \mu$ .
Theoretical Justification: This approach resums Next-to-Leading Order (NLO) counterterms into a single function. Unlike the standard Taruya-Nishimichi-Saito (TNS) model, which replaces specific correlators with a damping function (potentially violating momentum conservation at large scales), FolpsD maintains the full one-loop EFT structure and adds the damping as a prefactor to the nonlinear terms. This ensures compliance with Galilean invariance and momentum conservation constraints while allowing modeling up to higher wavenumbers ( $k \sim 0.3 \, h\text{Mpc}^{-1}$ ).

B. Bispectrum Modeling in the Sugiyama Basis

The code implements a tree-level galaxy bispectrum projected onto the tripolar spherical harmonics (Sugiyama) basis.

Basis: The bispectrum is decomposed into multipoles $B_{\ell_1 \ell_2 L}(k_1, k_2)$ using the Sugiyama basis, which is sensitive to second-order bias parameters ( $b_2, b_s$ ) that are poorly constrained by the power spectrum alone.
Damping in Bispectrum: A similar Lorentzian damping factor is applied to the bispectrum, dependent on the sum of squared projections of the triangle sides onto the LoS.
Alternative: The code also supports the Scoccimarro basis, though the Sugiyama basis is the primary focus for its signal-to-noise ratio.

C. Joint Analysis and Re-parametrization

Joint Likelihood: The framework performs a joint fit of the power spectrum and bispectrum multipoles.
Re-parametrization: To reduce degeneracies between nuisance parameters (bias, counterterms) and cosmological parameters, the authors use a re-parametrized basis where nuisance terms scale with the overall amplitude of the power spectrum ( $\sigma_8$ and Alcock-Paczynski amplitude $A_{AP}$ ).
Alcock-Paczynski (AP) Effect: The model includes full treatment of AP distortions for both $P(k)$ and $B(k)$ .

3. Key Contributions

FolpsD Code Release: A public code combining EFT power spectra with a tree-level bispectrum and phenomenological LoS damping.
Extended Scale Range: Demonstrates that the damped EFT model can reliably extend power spectrum analysis to $k_{max} \approx 0.301 \, h\text{Mpc}^{-1}$ (compared to the standard $0.2 \, h\text{Mpc}^{-1}$ ) without introducing significant biases for high signal-to-noise tracers.
Bispectrum Optimization: Shows that the bispectrum monopole can be robustly extended to $k_{max} \approx 0.24 \, h\text{Mpc}^{-1}$ in joint analyses, significantly tightening constraints.
Identification of Limitations: Provides a critical assessment of damping models, identifying that they can introduce biases for low signal-to-noise tracers (like QSOs) and in scenarios where the damping shape degenerates with specific cosmological features (e.g., massive neutrinos).

4. Results

A. Validation on Mocks (AbacusSummit)

The model was tested on 25 realizations of LRG (Luminous Red Galaxy) and QSO mocks.

LRGs (High S/N):
- Joint Analysis: The combination of FolpsD-Pk (damped power spectrum) and Bispectrum ( $B_{000}$ ) yields the tightest constraints.
- Improvement: Constraints on $A_s$ and $\omega_{cdm}$ improve by up to 30% compared to standard EFT power spectrum-only analyses.
- Bias: The joint analysis reduces parameter biases (measured by Figure of Bias, FoB) and improves the Figure of Merit (FoM) by ~14-30% over conservative cuts.
- Scale Extension: The bispectrum monopole can be extended to $k_{max} = 0.24 \, h\text{Mpc}^{-1}$ without bias, whereas standard EFT breaks down earlier.
QSOs (Low S/N):
- Limitation: For QSOs, the power spectrum is noise-dominated at smaller scales. The damping parameters become weakly constrained and absorb noise fluctuations, leading to biased cosmological parameter estimates (shifts $>1\sigma$ in $\omega_{cdm}$ ).
- Conclusion: Damping models require high signal-to-noise ratios to be reliable; they are not a universal fix for low-density tracers.

B. Application to DESI DR1 Data

The authors applied the power spectrum component of FolpsD to the DESI Data Release 1 (DR1) full-shape data.

$\Lambda$ CDM Constraints: Using FolpsD (up to $k_{max}=0.3$ ) compared to standard EFT (up to $k_{max}=0.2$ ), the constraints on $\sigma_8$ improved by 18.5%, and on $\Omega_m$ by 10.7%.
$w_0 w_a$ CDM Constraints: Using the ShapeFit formalism with FolpsD:
- Constraints on $w_0$ and $w_a$ tightened by 15% and 21%, respectively.
- The Figure of Merit for dark energy increased from 68 (EFT) to 161 (FolpsD).
- Significance: This analysis shows a deviation from constant dark energy ( $w = -1$ ) at slightly more than the $1\sigma$ level using full-shape information alone.

C. Neutrino Masses (Appendix C)

Degeneracy Issue: The authors found that the phenomenological damping factor strongly degenerates with the sum of neutrino masses ( $\sum m_\nu$ ) because both suppress the broadband power spectrum and damp BAO wiggles.
Result: In power-spectrum-only analyses, FolpsD yields weaker constraints on neutrino masses than standard EFT. However, including the bispectrum helps break this degeneracy, restoring the constraining power.

5. Significance and Conclusion

Synergy of Statistics: The paper demonstrates that joint power spectrum and bispectrum analyses are essential for maximizing the information content of DESI data. The bispectrum breaks degeneracies in bias parameters that the power spectrum cannot resolve.
Phenomenological vs. Systematic: The FolpsD approach successfully bridges the gap between strict EFT and phenomenological models. It allows for the inclusion of small-scale information ( $k > 0.2$ ) that is usually discarded, provided the tracer has sufficient signal-to-noise.
Caveats: The study highlights that "one-size-fits-all" damping models are dangerous for low-density tracers (QSOs) or specific cosmological scenarios (massive neutrinos) where the damping shape mimics the physical signal.
Future Impact: The results suggest that future DESI analyses can achieve significantly tighter constraints on dark energy and structure growth by adopting joint $P(k)+B(k)$ analyses with extended scale cuts, potentially revealing deviations from the standard $\Lambda$ CDM model.

The code is publicly available at https://github.com/cosmodesi/FolpsD.