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The impact of our peculiar motion on primordial non-Gaussianity measurements using the LIGER4GAL framework

This paper introduces the LIGER4GAL framework to accurately model linear-order relativistic redshift-space distortions in N-body simulations and demonstrates that neglecting the "finger-of-the-observer" effect can bias measurements of primordial non-Gaussianity ( $f_{\rm nl}$ ) by more than $1\sigma$ in a significant fraction of cosmic realizations.

Original authors: Bartolomeo Bottazzi Baldi, Mohamed Yousry Elkhashab, Daniele Bertacca, Cristiano Porciani

Published 2026-05-22

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CC BY 4.0

Original authors: Bartolomeo Bottazzi Baldi, Mohamed Yousry Elkhashab, Daniele Bertacca, Cristiano Porciani

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: Mapping the Universe with a Wobbly Ruler

Imagine you are trying to draw a map of a vast, foggy city at night. You want to know exactly where every streetlight (a galaxy) is located. To do this, you use a special ruler that measures distance based on how fast the light from the streetlight is stretching (redshift).

Usually, astronomers assume the city is perfectly flat and still. They use a standard ruler to convert the "stretch" of the light into a distance. However, the universe isn't perfectly flat or still. It's a bumpy, moving place.

The Problem:
When we look at distant galaxies, two things mess up our ruler:

The Galaxy's Movement: Galaxies aren't just sitting still; they are zooming around due to gravity. This is like a car driving toward you while honking its horn—the sound pitch changes. In space, this changes the galaxy's apparent position. Astronomers have known about this for a long time and usually correct for it.
The Observer's Movement (The "FOTO" Effect): This is the new focus of the paper. We (the Earth and our telescopes) are also moving through the universe. Imagine you are on a train looking out the window. If you are moving, the trees outside look like they are moving differently than if you were standing still. This "peculiar motion" of the observer creates a subtle distortion in how we see the entire map of the universe.

The paper argues that if we ignore this "Observer's Movement" (which the authors call the FOTO signal, short for Finger-Of-The-Observer), our map will be slightly wrong. And because we are trying to measure very subtle clues about the very beginning of the universe (called Primordial Non-Gaussianity or PNG), even a tiny error in the map can lead to a big mistake in our conclusions.

The Tool: LIGER4GAL (The "Cosmic Simulator")

To test how big this error is, the authors needed a way to simulate the universe with extreme precision. They created a new version of a software tool called LIGER (which stands for LIght cones with GEneral Relativity).

The Old Version (LIGER4DM): Think of this like a low-resolution video game. It could show the big picture of the universe well, but if you zoomed in on a specific neighborhood (small scales), the details were blurry and inaccurate. It treated galaxies like simple dots on a grid.
The New Version (LIGER4GAL): This is like upgrading to a 4K, high-definition simulation. Instead of just looking at the grid, this tool tracks individual "halos" (invisible bubbles of dark matter that hold galaxies) and the galaxies inside them. It applies the rules of Einstein's relativity directly to these specific objects.

Why this matters: The new tool allows them to create a "fake universe" that looks exactly like the real one, including the tricky relativistic distortions, all the way down to the smallest details.

The Experiment: Testing the "Observer's Motion"

The authors used their new high-definition simulator to create a fake galaxy survey that looks just like the real DESI survey (a massive project currently mapping millions of galaxies).

They ran the simulation twice:

Scenario A: They included the "Observer's Motion" (the FOTO effect) in the fake universe.
Scenario B: They ignored the "Observer's Motion," pretending the observer was perfectly still.

Then, they tried to measure a specific cosmic clue called $f_{NL}$ (a number that tells us about the physics of the Big Bang).

The Results:

The Bias: When they ignored the observer's motion, their measurement of the Big Bang clue ( $f_{NL}$ ) was wrong.
How Wrong? In about 40% of the possible universes they simulated, the error was large enough to shift their result by more than 1 standard deviation (a statistical way of saying "significantly wrong"). In 80% of the cases, the error was at least 0.25 standard deviations.
The Scale: This error gets worse the further out they look (at larger scales). If they include data from very far away (small $k$ values), the mistake becomes unavoidable.

The "Finger-of-the-Observer" Analogy

Imagine you are standing in a field of tall grass, and you are spinning around.

The Grass (Galaxies): They are stationary relative to the ground.
Your Spin (Observer's Motion): Because you are spinning, the grass looks like it is swaying in a specific pattern.
The Mistake: If you don't realize you are spinning, you might think the wind is blowing the grass in that specific pattern. You might conclude, "Ah, the wind is very strong!" when actually, it's just your own movement.

In cosmology, if we don't account for our own movement through space, we might think we are seeing a signature of the Big Bang (the wind) when it's actually just our own motion (the spin).

Conclusion: What Did They Find?

The paper concludes that for future, ultra-precise galaxy surveys (like DESI and Euclid), we must include the "Observer's Motion" in our models.

If we ignore it, we risk measuring the wrong value for the "clumpiness" of the early universe.
The new LIGER4GAL tool is essential because it allows scientists to simulate these effects accurately, ensuring that when we look at the real data, we aren't fooled by our own movement through the cosmos.

In short: To get the perfect map of the universe, we have to remember that the person holding the map is moving too.

Technical Summary: The Impact of Peculiar Motion on Primordial Non-Gaussianity Measurements Using LIGER4GAL

Problem Statement
Upcoming Stage-IV galaxy surveys (e.g., DESI, Euclid, SPHEREx) aim to map the large-scale structure (LSS) of the Universe with unprecedented precision to constrain fundamental physics, including Dark Energy, Dark Matter, and primordial non-Gaussianity (PNG). A critical challenge in these analyses is the accurate modeling of redshift-space distortions (RSDs). While standard analyses routinely account for the leading-order Kaiser effect (peculiar velocities of sources), they often neglect relativistic RSDs. These relativistic effects, which include integrated terms like weak lensing, the integrated Sachs-Wolfe effect, and the "finger-of-the-observer" (FOTO) effect (sourced by the observer's peculiar velocity), become increasingly significant on ultra-large scales.

The paper highlights a specific risk: relativistic effects, particularly the FOTO signal, share similar scale dependencies with the local PNG signature (parameterized by $f_{\text{nl}}$ ). Neglecting these relativistic contributions in theoretical models can introduce systematic biases in the measurement of $f_{\text{nl}}$ and other cosmological parameters, potentially leading to false detections or incorrect constraints. Previous methods for generating mock catalogs with relativistic effects (LIGER4DM) relied on low-resolution simulations and linear biasing, failing to accurately describe clustering on quasi-linear and non-linear scales where modern analyses operate.

Methodology
To address these limitations, the authors introduce LIGER4GAL, an updated implementation of the LIGER (LIght cones with GEneral Relativity) method.

LIGER4GAL Framework: Unlike its predecessor (LIGER4DM), which applied coordinate transformations to dark matter (DM) particles and used a linear biasing scheme to generate galaxy fields, LIGER4GAL operates directly on high-resolution halo catalogs.
- It utilizes halo merger trees and gravitational potential fields derived from high-resolution N-body simulations (specifically the Huge MultiDark Planck simulation, HMDPL).
- It applies the full linear-order relativistic coordinate map (including position shifts and magnification) directly to halos.
- It subsequently populates these halos with galaxies using a Halo Occupation Distribution (HOD) model consistent with DESI Luminous Red Galaxies (LRGs). Crucially, it corrects the positions and magnifications of satellite galaxies for their peculiar velocities relative to their host halos, ensuring consistency with the relativistic treatment on sub-halo scales.
Mock Generation: The authors generated four types of mock catalogs from the HMDPL simulation ( $4 \text{ Gpc}/h$ box, $4096^3$ particles) to isolate specific relativistic effects:
- R: Real-space (no RSDs).
- V: Includes only source peculiar velocities (standard Kaiser effect).
- G: Includes all linear relativistic RSDs, assuming the observer is at rest in the Cosmic Rest Frame (CRF).
- O: Includes all linear relativistic RSDs plus the observer's peculiar velocity (FOTO effect), using the magnitude and direction measured by the Planck satellite.
Analysis: The authors performed cosmological parameter inference on these mocks using two approaches:
- Local PNG Measurement: Fitting the power spectrum multipoles (monopole and quadrupole) to extract $f_{\text{nl}}$ , comparing results from catalogs with and without the full relativistic treatment.
- Full-Shape Analysis: Using the Effective Field Theory (EFT) of LSS to constrain cosmological parameters ( $A_s, \omega_c, h$ ) in a $\Lambda$ CDM model.

Key Contributions

LIGER4GAL Implementation: A novel pipeline that integrates relativistic RSDs directly at the tracer level of high-resolution simulations, preserving non-linear clustering accuracy while maintaining linear-order relativistic corrections.
Relativistic Toolkit: A companion toolkit (compatible with halotools) for populating halos with galaxies that consistently applies relativistic corrections to both line-of-sight positions and magnification bias, accounting for satellite peculiar velocities.
Quantification of FOTO Bias: A rigorous assessment of how the observer's peculiar motion (FOTO effect) biases $f_{\text{nl}}$ measurements, demonstrating that this effect varies significantly across different realizations of the universe.

Results

Validation: LIGER4GAL successfully reproduces the expected non-linear clustering signal, outperforming LIGER4DM on quasi-linear scales where the latter overestimates clustering due to resolution and linear bias limitations.
FOTO Signal Detection: The FOTO signal was successfully recovered in the power spectrum monopole. The signal is oscillatory and its amplitude depends on the survey geometry (full-sky vs. masked) and the specific realization of the universe.
Bias in $f_{\text{nl}}$ :
- Neglecting the FOTO effect introduces a bias in $f_{\text{nl}}$ measurements.
- For a DESI-like partial-sky survey, omitting the FOTO effect can bias $f_{\text{nl}}$ by more than $1\sigma_{f_{\text{nl}}}$ in approximately 40% of universe realizations if scales down to $k_{\text{min}} = 0.0015 \, h/\text{Mpc}$ are included.
- In 80% of realizations, the bias exceeds $0.25\sigma_{f_{\text{nl}}}$ .
- The bias is realization-dependent; some realizations show negligible bias, while others (strong FOTO realizations) show shifts up to $1.5\sigma_{f_{\text{nl}}}$ .
Full-Shape Analysis: Relativistic RSDs, particularly strong FOTO signals, induce systematic shifts in the inferred parameters $A_s$ , $\omega_c$ , and $h$ . However, these biases are largely removed when excluding the largest scales ( $k < 4 \times 10^{-3} \, h/\text{Mpc}$ ) typically used in full-shape analyses.

Significance and Claims
The paper claims that as future surveys probe larger volumes and include increasingly large scales (e.g., DESI Year 5, Euclid DR3), the contribution of the observer's peculiar motion (FOTO) will become progressively more significant. The authors assert that:

Current standard modeling, which often neglects relativistic RSDs beyond the source peculiar velocity, risks systematic biases in PNG measurements that could mimic or mask primordial signals.
The LIGER4GAL framework provides a robust, high-fidelity method for generating mock catalogs that include these effects, enabling realistic assessments of systematic biases.
While the FOTO signal can be marginalized or modeled, its omission in current analyses of DESI-like data (which typically cut off at $k_{\text{min}} \approx 6 \times 10^{-3} \, h/\text{Mpc}$ ) likely results in only minor biases for current datasets, but this will change as analyses extend to smaller $k$ .
The toolkit allows for the generation of light cones with relativistic RSDs for any tracer population, provided sufficiently large simulations with halo merger trees are available, facilitating the preparation for next-generation cosmological constraints.

The authors conclude that incorporating these relativistic effects into both power-spectrum models and covariance matrices is essential for the precision cosmology era, though they note that analytic modeling of these effects remains challenging due to the complexity of survey geometry mixing multipoles.

The Big Picture: Mapping the Universe with a Wobbly Ruler

The Tool: LIGER4GAL (The "Cosmic Simulator")

The Experiment: Testing the "Observer's Motion"

The "Finger-of-the-Observer" Analogy

Conclusion: What Did They Find?

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