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Testing Scale-Dependent Modified Gravity with DESI DR1

Using DESI Data Release 1 power spectrum measurements within an EFT framework, this study finds no evidence for deviations from General Relativity and establishes a stringent constraint of $\log_{10} |f_{R_0}| < -3.60$ on the range of a hypothetical fifth force, demonstrating that the modified gravity parameters are largely orthogonal to standard cosmological parameters and robust against variations in analysis choices.

Original authors: D. Gonzalez (DESI Collaboration), G. Niz (DESI Collaboration), A. Aviles (DESI Collaboration), C. Garcia-Quintero (DESI Collaboration), H. E. Noriega (DESI Collaboration), J. Aguilar (DESI Collaborati

Published 2026-04-30

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Original authors: D. Gonzalez (DESI Collaboration), G. Niz (DESI Collaboration), A. Aviles (DESI Collaboration), C. Garcia-Quintero (DESI Collaboration), H. E. Noriega (DESI Collaboration), J. Aguilar (DESI Collaboration), S. Ahlen (DESI Collaboration), D. Bianchi (DESI Collaboration), D. Brooks (DESI Collaboration), T. Claybaugh (DESI Collaboration), A. de la Macorra (DESI Collaboration), A. de Mattia (DESI Collaboration), P. Doel (DESI Collaboration), S. Ferraro (DESI Collaboration), J. E. Forero-Romero (DESI Collaboration), E. Gaztañaga (DESI Collaboration), S. Gontcho A Gontcho (DESI Collaboration), G. Gutierrez (DESI Collaboration), C. Hahn (DESI Collaboration), K. Honscheid (DESI Collaboration), D. Huterer (DESI Collaboration), M. Ishak (DESI Collaboration), R. Joyce (DESI Collaboration), S. Juneau (DESI Collaboration), R. Kehoe (DESI Collaboration), D. Kirkby (DESI Collaboration), M. Landriau (DESI Collaboration), L. Le Guillou (DESI Collaboration), M. E. Levi (DESI Collaboration), M. Manera (DESI Collaboration), A. Meisner (DESI Collaboration), R. Miquel (DESI Collaboration), S. Nadathur (DESI Collaboration), W. J. Percival (DESI Collaboration), I. Pérez-Ràfols (DESI Collaboration), G. Rossi (DESI Collaboration), L. Samushia (DESI Collaboration), E. Sanchez (DESI Collaboration), D. Schlegel (DESI Collaboration), H. Seo (DESI Collaboration), J. Silber (DESI Collaboration), D. Sprayberry (DESI Collaboration), G. Tarlé (DESI Collaboration), B. A. Weaver (DESI Collaboration), R. Zhou (DESI Collaboration)

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 fabric called "spacetime." For nearly a century, our best map of how this fabric behaves comes from Albert Einstein's theory of General Relativity (GR). It's like a trusted rulebook that explains how gravity works: massive objects like stars and galaxies bend the fabric, and everything else follows those curves.

However, scientists have noticed some strange things about the universe's expansion that the standard rulebook doesn't perfectly explain. This has led to the idea of "Modified Gravity" (MG). Think of MG as a new, slightly different rulebook that suggests gravity might have a secret "fifth force" or a hidden switch that turns on under specific conditions.

The New Tool: DESI
To test these new rulebooks, the authors used a massive telescope instrument called DESI (Dark Energy Spectroscopic Instrument). Imagine DESI as a super-powered camera that doesn't just take pictures of galaxies, but measures their "redshift" (how fast they are moving away from us) with incredible precision. It has mapped millions of galaxies, creating a 3D map of the universe's history.

The Mystery: A Hidden Scale
The specific theory the authors tested suggests that gravity isn't the same everywhere.

The Analogy: Imagine gravity is like a radio signal. In the standard rulebook (General Relativity), the signal is strong and clear everywhere. In this new theory, there's a "static zone." If you are very close to a galaxy (small scale), the signal is clear. But if you are far away, or if you look at a specific range of distances, a hidden "fifth force" might kick in, making gravity stronger or weaker than Einstein predicted.
The "Fifth Force": The authors looked for a specific physical scale (a specific distance) where this extra force would start to matter. They called this the "Yukawa scale." It's like looking for the exact distance where a new type of magnet starts to pull on a paperclip, something standard magnets don't do.

The Experiment: Checking the Pattern
The researchers looked at the "clumping" of galaxies. In the universe, galaxies aren't scattered randomly; they form a cosmic web. The way they cluster together creates a specific pattern (a power spectrum).

If Einstein is right, the pattern looks one way.
If this new "fifth force" exists, the pattern would change at specific distances (scales), like a ripple in a pond that only appears after a certain distance from the stone.

The authors used a sophisticated computer model (an "Effective Field Theory") to predict what the galaxy patterns would look like if this fifth force existed. They then compared these predictions against the actual data from DESI.

The Results: The Rulebook Stands
After crunching the numbers, the result was clear: The data matches Einstein's rulebook perfectly.

No New Force Found: They found no evidence of this mysterious fifth force or the new scale where gravity changes.
The Constraint: They didn't just say "it's not there." They set a very strict limit. They calculated that if this extra force does exist, it must be so weak or act over such a tiny distance that it's effectively invisible to our current tools.
- They found that if this force exists, it can only operate over distances smaller than about 18 million light-years (17.81 Megaparsecs).
- In terms of the "particle" that would carry this force, it must be heavier than a specific tiny amount (which makes it very hard to detect).

Why This Matters
The paper emphasizes that this is a very robust test.

Orthogonality: The new gravity parameter they tested is "orthogonal" to the other numbers in the universe (like how much dark matter there is). This means testing for this new force didn't mess up their calculations for the rest of the universe. They could look for the new force without breaking the old model.
Independence: They tested this using just the galaxy clustering data. They didn't need to mix in other types of data (like the Cosmic Microwave Background) to get a result, which makes the finding very clean.
Future Proofing: They checked if changing the "background" of the universe (like assuming dark energy changes over time) or looking at different types of galaxies changed the result. It didn't. The conclusion remains: General Relativity still holds up.

In Summary
The authors used the most detailed map of the universe ever created (DESI) to look for a hidden "fifth force" that would change how gravity works at certain distances. They found nothing. The universe, at least at the scales they tested, still follows Einstein's rules. If this new force exists, it is hiding in a very small, very specific corner of the universe that our current instruments haven't been able to see yet.

1. Problem Statement

The paper addresses the need to test deviations from General Relativity (GR) that introduce scale-dependent modifications to gravity. Unlike scale-independent modifications (which affect the growth rate uniformly or via a constant shift), scale-dependent theories (such as $f(R)$ gravity) introduce a new physical length scale, $\lambda$ (or wavenumber $k_{MG}$ ). Below this scale, a "fifth force" mediated by a massive scalar field enhances gravitational clustering, while on larger scales, the theory recovers standard GR.

While previous DESI analyses have tested scale-independent deviations, this work focuses on the Full-Shape (FS) of the galaxy power spectrum to constrain these scale-dependent effects. The primary challenge is distinguishing these modifications from standard cosmological parameters and nuisance parameters (bias, shot noise) without introducing "projection effects" (biases in inferred parameters due to degeneracies with unconstrained nuisance parameters).

2. Methodology

Data Sources

Primary Data: DESI Data Release 1 (DR1), utilizing the monopole and quadrupole moments of the power spectrum for four tracer types: Bright Galaxy Survey (BGS), Luminous Red Galaxies (LRG), Emission Line Galaxies (ELG), and Quasars (QSO). The analysis covers the redshift range $0.1 < z < 2.1$ .
External Data:
- BAO: DESI DR1 Baryon Acoustic Oscillation data.
- CMB: Compressed geometric priors from Planck ( $\theta_*, \omega_b, \omega_{bc}$ ) and a prior on the spectral index $n_s$ .
- SNIa: Dark Energy Survey Year 5 (DES-Y5) and other supernova datasets (DES-Dovekie, Pantheon+, Union3) to test background evolution robustness.
- BBN: Priors on baryon density $\omega_b$ .

Theoretical Framework

Effective Field Theory (EFT): The analysis employs the EFT of Large Scale Structure (LSS) to model the power spectrum up to mildly non-linear scales ( $k \lesssim 0.2 \, h\text{Mpc}^{-1}$ ).
Scale-Dependent Growth: The model incorporates a scale-dependent growth rate $f(k,t)$ derived from a Yukawa-like potential:
$V(r) \sim \frac{G_N 2\beta^2}{r} e^{-m_\phi r}$
where $m_\phi$ is the mass of the scalar mediator and $\beta^2 = 1/6$ (coupling strength $2\beta^2 = 1/3$ ).
Hu-Sawicki (HS) Mapping: The Yukawa potential is mapped to the Hu-Sawicki $f(R)$ model. The mass scale $m_\phi$ is related to the HS parameters ( $n, f_{R0}$ ) and the background cosmology via:
$m_\phi^2(a) = \frac{H_0^2}{2|f_{R0}|} \frac{(\Omega_m a^{-3} + 4\Upsilon(a))^{n+2}}{(\Omega_m + 4\Upsilon(a_0))^{n+1}}$
Here, $f_{R0} \equiv df(R)/dR|_{today}$ controls the range of the fifth force, and $n$ modulates its time evolution.
fkpt Approximation: The authors use the fkpt code (adapted for the desilike pipeline) to compute loop integrals. This approach explicitly tracks the $k$ -dependence of the growth function and growth rate in the perturbative kernels, essential for scale-dependent MG.
Analysis Strategy:
- Baseline Model: Fixed $n=1$ (standard HS choice), $\Lambda$ CDM background, $k_{max} = 0.17 \, h\text{Mpc}^{-1}$ (conservative cut to avoid screening non-linearities).
- Extensions: Varying $n$ , changing background to $w_0w_a$ CDM, including neutrino mass sum ( $\sum m_\nu$ ), and testing different $k_{max}$ cuts.

3. Key Contributions

First FS Constraints with DESI DR1: This is the first application of DESI DR1 Full-Shape data specifically to constrain scale-dependent modified gravity using the EFT framework.
Orthogonality of Parameters: The study demonstrates that the modified gravity parameter $f_{R0}$ is largely orthogonal to standard cosmological parameters ( $H_0, \Omega_m, \ln A_s$ ) and nuisance parameters. This implies that adding MG parameters does not introduce significant new projection effects or bias the standard cosmological inference.
Robustness Checks: The authors validate the model by:
- Varying the power index $n$ (finding $n \approx 1.4$ is consistent with $n=1$ ).
- Changing the background dark energy equation of state ( $w_0w_a$ ).
- Testing different maximum wavenumbers ( $k_{max}$ ).
- Analyzing individual redshift bins separately.
Neutrino Degeneracy: The paper quantifies the degeneracy between the MG parameter $f_{R0}$ and the sum of neutrino masses, finding it to be small (~10% degradation in constraints).

4. Key Results

Constraints on Modified Gravity

The analysis finds no evidence for deviations from GR. The constraints on the HS parameter $f_{R0}$ (at 95% Confidence Level) are:

DESI DR1 (FS only): $|f_{R0}| < 2.60 \times 10^{-5}$
DESI DR1 (FS + BAO): $|f_{R0}| < 2.52 \times 10^{-5}$
With CMB compressed priors: $|f_{R0}| < 2.50 \times 10^{-5}$
With DES-Y5 SNIa: $|f_{R0}| < 2.76 \times 10^{-5}$

These constraints translate to an upper bound on the interaction range of the fifth force at redshift zero:
$\lambda < 17.81 \, \text{Mpc}$
Or equivalently, a lower bound on the scalar field mass:
$m_\phi > 3.60 \times 10^{-31} \, \text{eV}$

Impact of Extensions

Free $n$ : Allowing $n$ to vary yields $n = 1.41 \pm 0.52$ , consistent with the baseline $n=1$ .
$k_{max}$ Sensitivity: Increasing $k_{max}$ from $0.17$ to $0.20 \, h\text{Mpc}^{-1}$ improves the $f_{R0}$ constraint by ~35%, suggesting that higher- $k$ modes contain significant information, though the baseline cut is chosen to remain safely within the regime where EFT counterterms can absorb screening effects.
Background Evolution: Switching to a dynamical dark energy ( $w_0w_a$ ) background relaxes the tension between DESI and CMB data but does not significantly alter the MG constraints.

5. Significance

Validation of GR: The results strongly support General Relativity on cosmological scales up to $z \sim 2$ , ruling out a wide class of unscreened $f(R)$ models that attempt to explain cosmic acceleration without dark energy.
Methodological Benchmark: The paper establishes a robust pipeline for testing scale-dependent gravity using Full-Shape analyses, demonstrating that such tests can be performed without compromising the precision of standard cosmological parameter estimation.
Future Prospects: The authors note that while current constraints are limited by the maximum accessible wavenumber ( $k_{max}$ ), future DESI releases (DR2 and beyond) with larger volumes and higher statistics will probe smaller scales, potentially tightening these bounds further. The inclusion of higher-order statistics (bispectrum) is also highlighted as a future avenue for enhanced sensitivity.

In summary, this work provides the tightest cosmological constraints to date on the range of a hypothetical fifth force using DESI data, confirming that General Relativity remains the dominant description of gravity on scales up to $\sim 18$ Mpc.