🔭 astrophysics

Effects of Symmetron on growth and RSD multipoles

This study employs the fk-PT perturbation theory within the FOLPS-nu code to analyze Symmetron modified gravity effects on cosmic structure formation and redshift-space distortion multipoles, validating the methodology's ability to recover General Relativity limits from mock data and confirming its readiness for testing modified gravity models against current and future galaxy surveys.

Original authors: Gerardo Morales-Navarrete, Jorge L. Cervantes-Cota

Published 2026-02-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Gerardo Morales-Navarrete, Jorge L. Cervantes-Cota

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, expanding balloon. For decades, scientists have used a standard recipe called $\Lambda$ CDM to explain how this balloon inflates and how the dots on it (galaxies) clump together. This recipe works great, but it relies on a mysterious ingredient called "Dark Energy" that we don't fully understand. It's like baking a cake and having to add a secret spice that you can't taste or measure, just to make it rise correctly.

Recently, new data suggests this standard recipe might be slightly off. So, scientists are testing Modified Gravity (MG) theories. Think of these as new recipes that tweak the laws of physics (gravity) itself to explain the expansion, rather than adding a mysterious spice.

This paper is about testing two specific new recipes: the Symmetron model and the Hu-Sawicki $f(R)$ model. Here is a simple breakdown of what they did and what they found:

1. The Problem: Gravity's "Zoom" Feature

In our standard universe, gravity works the same way whether you are looking at a single star or a whole galaxy cluster. But in these new models, gravity has a "zoom" feature.

The Analogy: Imagine gravity is a camera lens. In the standard model, the lens is fixed. In the new models, the lens changes its focus depending on how close you are to the object.
- Close up (like inside our Solar System): The lens acts normal so we don't break the laws of physics we already know (like planets orbiting the sun).
- Far away (like between galaxy clusters): The lens zooms in, making gravity stronger. This extra strength helps galaxies clump together faster, which might explain the universe's expansion without needing that "secret spice."

2. The Experiment: Listening to the Cosmic Symphony

The authors wanted to see how these new gravity recipes change the way galaxies move and cluster. They looked at something called Redshift-Space Distortions (RSD).

The Analogy: Imagine a crowded dance floor. If everyone is just standing still, you see a perfect circle of people. But if people are dancing and moving toward the center (clumping), the circle gets squished and distorted.
Scientists measure these "squishes" (distortions) to figure out how fast galaxies are falling together. They broke this data down into two main shapes:
- The Monopole (The Round Shape): How much the overall cluster is squished.
- The Quadrupole (The Oval Shape): How stretched out the cluster looks.

They used a sophisticated computer tool (called FOLPS-nu) to calculate what these shapes should look like if the Symmetron or $f(R)$ models were true, and compared them to the standard recipe.

3. The Results: A Tale of Two Shapes

When they ran the numbers at the current time (redshift $z=0$ ):

The Monopole (Roundness): Both new models predicted galaxies would clump less than the standard model. However, the Symmetron model was very close to the standard recipe, almost indistinguishable.
The Quadrupole (Ovalness): Here, the new models acted differently. They predicted the clusters would be more stretched out than the standard model.

The Takeaway: The Symmetron model is a "quiet" player. It doesn't change the overall clumping much, but it does change the shape of the clusters in a way that is different from the standard model.

4. The Safety Check: The "Fake" Universe

Before they could trust their results with real data, they had to prove their computer code worked.

The Problem: They didn't have a perfect computer simulation of a "Symmetron universe" to test against.
The Solution: They used "EZMocks"—fake data generated from the standard universe (General Relativity).
The Test: They fed this fake standard data into their Symmetron code.
The Result: The code correctly said, "Hey, this looks like the standard universe!" It successfully recovered the standard physics (where the new gravity effects are zero).
Why this matters: It's like testing a new metal detector on a beach where you know there are no gold coins. If the detector beeps, it's broken. If it stays silent, it's working. Since their code stayed silent on the fake data, they know it's reliable enough to use on real data from future telescopes.

Summary

This paper is a "dress rehearsal" for future space missions. The authors built a new tool to test if gravity works differently on a cosmic scale. They found that the Symmetron model is a subtle alternative to the standard universe—it changes the shape of galaxy clusters in a unique way but stays very close to what we already know. Most importantly, they proved their tool works by successfully identifying a "standard" universe when they tried to analyze it with their new model.

Now, they are ready to take this tool out and analyze real data from upcoming galaxy surveys to see if the universe is actually following this new, subtle recipe.

1. Problem Statement

The standard $\Lambda$ CDM cosmological model, while successful, relies on the cosmological constant ( $\Lambda$ ) to explain cosmic acceleration, a hypothesis facing theoretical challenges. Recent observational data from surveys like DESI and DES suggest tensions with $\Lambda$ CDM (up to $4.2\sigma$ ), pointing toward the need for dynamical dark energy or Modified Gravity (MG) theories.

The specific challenges addressed in this work include:

Testing MG Models: There is a need to rigorously test alternative gravity models, specifically the Symmetron and Hu-Sawicki $f(R)$ models, which incorporate screening mechanisms to satisfy solar system constraints while predicting distinct large-scale structure clustering.
Scale-Dependent Growth: Unlike $\Lambda$ CDM, MG models introduce a scale dependence in the growth rate of cosmic structures ( $f(k, a)$ ). This complicates the calculation of cosmological observables, particularly the Redshift-Space Distortion (RSD) multipoles, making efficient comparison with observational data difficult.
Lack of Simulations: Validating MG pipelines against high-precision simulations is hindered by the lack of suitable Symmetron simulations that cover non-linear 1-loop effects and infrared resummation schemes.

2. Methodology

The authors developed a computational pipeline to analyze the power spectrum multipoles in MG models using the following approach:

Theoretical Framework:
- Growth Equation: They utilized a scale-dependent growth equation where the growth rate $f$ depends on the wavenumber $k$ and scale factor $a$ . The equation incorporates the modification function $\mu(k, a)$ , which enhances the effective matter density contrast.
- $f_k$ -PT Approach: To handle the computational inefficiency of full scale dependence, they employed the $f_k$ -PT (perturbation theory) approximation. This method retains the scale dependence in the linear growth rate while using standard $\Lambda$ CDM kernels for higher-order terms. This approach was previously validated for $\Lambda$ CDM + neutrinos and $f(R)$ models.
- Code Implementation: The calculations were implemented in the FOLPS-nu code, which computes the full 1-loop power spectrum including Infrared (IR) Resummation.
Models Analyzed:
- Symmetron Model: A scalar-tensor theory with a screening mechanism.
- Hu-Sawicki $f(R)$ Model: Specifically the $F6$ variant.
- Reference: Standard $\Lambda$ CDM model.
Parameters:
- Cosmological parameters: $\{\Omega_m, \Omega_b, h, n_s\} = \{0.281, 0.046, 0.697, 0.971\}$ .
- Nuisance parameters: EFT counterterms, bias parameters ( $b_1, b_2, b_{s2}, b_{3nl}$ ), and shot noise.
- Symmetron specific parameters: $\beta_0 = 1$ , $m_0 = 1$ , $a_{ssb} = 0.5$ .
Validation Strategy:
- Due to the unavailability of suitable Symmetron simulations, the authors used General Relativity (GR) mock catalogs (EZMocks) to validate their pipeline.
- They performed a Markov Chain Monte Carlo (MCMC) analysis on these GR mocks using the Symmetron model framework to verify if the pipeline could correctly recover the GR limit (where the MG coupling parameter $\beta_0 \to 0$ ).

3. Key Contributions

Implementation of Symmetron in FOLPS-nu: The work extends the FOLPS-nu code to handle the Symmetron model using the $f_k$ -PT approximation, enabling the computation of 1-loop RSD multipoles for this specific MG theory.
Validation Protocol: The authors established a robust validation method using GR mocks to test MG pipelines in the absence of dedicated MG simulations, proving that the methodology can distinguish between MG and GR limits.
Comparative Analysis: The study provides a direct comparison of the monopole ( $\ell=0$ ) and quadrupole ( $\ell=2$ ) power spectra between Symmetron, $f(R)$ , and $\Lambda$ CDM at $z=0$ .

4. Results

Power Spectrum Multipoles ( $z=0$ ):
- Monopole ( $\ell=0$ ): Both MG models show suppression compared to $\Lambda$ CDM. However, the Symmetron model is closer to the $\Lambda$ CDM prediction than the Hu-Sawicki $F6$ model.
- Quadrupole ( $\ell=2$ ): Exhibits the opposite behavior. Both MG models show an enhancement (larger values) compared to $\Lambda$ CDM.
- Scale Dependence: The deviations are most prominent in the range $k < 0.25 \, h \, \text{Mpc}^{-1}$ .
MCMC Validation:
- When the Symmetron pipeline was applied to GR mock data (EZMocks), the MCMC analysis successfully recovered the expected GR limit.
- The estimated value for the MG coupling parameter $\beta_0$ was found to be less than $10^{-7}$ at a 65% confidence level, effectively zero.
- The confidence contours centered on the expected $\Lambda$ CDM values, confirming that the pipeline does not introduce systematic biases when analyzing GR data with an MG model.

5. Significance

Methodological Viability: The successful recovery of the GR limit from Symmetron analysis on mock data confirms that the pipeline is robust and ready for application to real observational data.
Future Surveys: The work prepares the community to test MG models against current and near-future galaxy surveys (e.g., DESI, Euclid, LSST). By demonstrating that 1-loop RSD multipoles can be accurately computed and constrained for Symmetron models, the study opens the door to tighter constraints on modified gravity theories.
Differentiation: The distinct behaviors of the monopole and quadrupole in Symmetron vs. $f(R)$ models provide specific observational signatures that can be used to distinguish between different MG theories in future data analysis.