🔭 astrophysics

From photometric surveys to HI intensity mapping: Improving constraints on magnification biases while testing gravity

This paper demonstrates that combining photometric galaxy surveys with HI intensity mapping via a multi-tracer approach significantly improves constraints on magnification bias parameters and the Weyl potential amplitude, thereby enabling high-precision tests of general relativity on cosmological scales.

Original authors: T. Sinde, J. Fonseca

Published 2026-04-01

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: T. Sinde, J. Fonseca

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, three-dimensional spiderweb made of invisible dark matter. Galaxies are like tiny spiders sitting on this web. To understand how the web is built and how it behaves, astronomers try to map where these spiders are located.

However, there's a catch. The "camera" we use to take pictures of these spiders isn't perfect. As the light from the spiders travels across the universe to reach us, it passes through massive clumps of matter (like other galaxies or dark matter). These clumps act like cosmic magnifying glasses, bending the light. This is called gravitational lensing.

This bending does two tricky things:

It distorts the shape of the spiders (making them look stretched).
It changes how many spiders we see in a specific area. Some get magnified and become visible; others get demagnified and disappear. This is called magnification bias.

For a long time, astronomers have used "photometric surveys" (taking pictures in broad colors) to map these spiders. But because these pictures are a bit blurry regarding distance, it's hard to separate the real clustering of spiders from the fake clustering caused by the magnifying glasses.

The New Idea: The "Multi-Tracer" Technique

This paper proposes a clever solution: combine two different types of surveys to get a clearer picture. Think of it like trying to listen to a conversation in a noisy room.

Survey A (The Photographers): These are the big optical telescopes (like DES, LSST, and Euclid). They take great pictures of millions of galaxies but have blurry distance estimates. They are like someone trying to hear a conversation from far away; they see the people clearly but can't tell exactly how far away they are.
Survey B (The Radio Listeners): These are new radio telescopes (like MeerKLASS and SKAO) that listen to the "hum" of neutral hydrogen gas (Hi) filling the universe. They don't see individual galaxies, but they hear the gas very precisely in terms of distance. They are like someone standing right next to the conversation; they know exactly how far away the speakers are, even if they can't see their faces clearly.

The authors call this the "Multi-Tracer" technique. By overlapping the area where both surveys look at the sky, they can use the precise distance data from the Radio Listeners to correct the blurry distance data from the Photographers.

What Did They Find?

The researchers used a mathematical tool (called a "Fisher Matrix," which is like a crystal ball for predicting how well future experiments will work) to simulate this combination. Here is what they discovered:

Breaking the Magic Trick: When they combined the two surveys, they could finally separate the "real" galaxy distribution from the "magnification" tricks. It's like putting on 3D glasses; the flat, confusing image suddenly pops out in depth.
Testing Gravity: One of the main goals was to test Einstein's theory of General Relativity. They looked for a specific number (called $\beta$ ) that tells us if gravity behaves exactly as Einstein predicted or if it's slightly different (which would mean "Modified Gravity").
- The Result: Using just the Photographers, the uncertainty on this number was about 20%. But when they added the Radio Listeners, the uncertainty dropped to less than 1%. In some cases, the improvement was a factor of 50! It's the difference between guessing the weight of a car and weighing it on a precision scale.
Measuring the Lens: They also improved their ability to measure the "magnification bias" (how much the lens is distorting things). While the improvement wasn't as huge as for gravity, it was still significant (2 to 8 times better).

Why Does This Matter?

Imagine you are trying to figure out the rules of a game, but the scoreboard is broken and sometimes adds extra points randomly.

Old Way: You try to guess the rules while ignoring the broken scoreboard. You get a rough idea, but you might be wrong about the fundamental rules.
New Way: You bring in a second observer who has a perfect stopwatch. By comparing the two, you can figure out exactly how the scoreboard is broken. Once you know how it's broken, you can fix the data and finally understand the true rules of the game.

In this cosmic game, the "rules" are the laws of gravity. By combining optical and radio surveys, we can now test Einstein's theories with incredible precision. If we find even a tiny crack in the rules, it could mean there is new physics waiting to be discovered.

The Bottom Line

This paper shows that by pairing our best "camera" telescopes with our best "radio" telescopes, we can turn the universe's natural magnifying glasses from a nuisance into a powerful tool. This allows us to map the invisible web of the universe with unprecedented clarity and test the very fabric of reality.

1. Problem Statement

The observed large-scale structure (LSS) of the Universe is distorted by General Relativity (GR) effects, specifically gravitational lensing. While weak lensing (shear) is widely used to test gravity, the paper focuses on magnification lensing in galaxy number counts.

The Challenge: In photometric galaxy surveys, the observed number density of galaxies is biased by magnification. This effect depends on the magnification bias ( $s_G(z)$ ), which is the slope of the luminosity function, and the Weyl potential ( $\Phi + \Psi$ ), which encodes the theory of gravity.
The Degeneracy: The magnification bias parameter $s_G(z)$ and the gravity probe parameter $\beta$ (which scales the Weyl potential) are naturally degenerate when analyzing a single tracer (e.g., galaxies alone). This makes it difficult to simultaneously constrain the bias and test for deviations from GR (where $\beta \neq 1$ ).
The Limitation of Current Surveys: Photometric surveys (like DES, LSST, Euclid) suffer from large photometric redshift ($photo-z$) uncertainties, which smear information along the line of sight. Conversely, while HI Intensity Mapping (IM) provides precise spectroscopic redshifts, it currently lacks the angular resolution of optical surveys.

2. Methodology

The authors employ a Fisher matrix formalism to forecast the precision of future constraints on cosmological parameters.

Theoretical Framework:
- They utilize the linearly perturbed FLRW metric in the Newtonian gauge, introducing a parameter $\beta$ to test modified gravity ( $\Phi + \Psi = \beta \times \text{GR prediction}$ ).
- They model the number density contrast ( $\Delta N$ ) including contributions from intrinsic clustering, Redshift Space Distortions (RSD), and lensing magnification.
- The lensing term is modulated by $s_G(z)$ and $\beta$ . Notably, they highlight that for HI Intensity Mapping, the lensing contribution to the signal is negligible at linear order due to the conservation of surface brightness, making HI an ideal "clean" tracer to break degeneracies with galaxies.
Statistical Estimators:
- The study compares two estimators: the Angular Power Spectrum ( $C_\ell$ ) and the Angular Correlation Function ( $w(\theta)$ ).
- They conclude that $C_\ell$ is computationally superior due to its block-diagonal covariance matrix, avoiding the numerical instability of inverting the dense covariance matrices required for $w(\theta)$ .
Survey Specifications:
- Photometric Surveys: Modeled after DES (Dark Energy Survey), LSST (Legacy Survey of Space and Time), and Euclid. These provide high galaxy counts but broad redshift bins.
- HI Intensity Mapping Surveys: Modeled after MeerKLASS (MeerKAT) and SKAO (Square Kilometre Array). These provide high redshift precision but cover different sky areas.
- Multi-Tracer Technique: The core methodology involves cross-correlating the galaxy surveys with HI surveys in the overlapping sky area. This exploits the fact that while both tracers trace the same underlying dark matter, they have different biases and noise properties.
Parameters Constrained:
- Standard cosmological parameters ( $H_0, \Omega_m, \Omega_b, w, A_s, n_s$ ).
- Target Parameters: The gravity probe $\beta$ (fiducial value 1) and the magnification bias $s_G(z)$ for each redshift bin.

3. Key Contributions

Validation of Multi-Tracer Synergy: The paper demonstrates that combining photometric galaxy surveys with HI IM surveys is a powerful method to break the degeneracy between magnification bias ( $s_G$ ) and the gravitational potential amplitude ( $\beta$ ).
Estimator Comparison: It provides a practical comparison showing that while $C_\ell$ and $w(\theta)$ yield similar constraints, $C_\ell$ is the preferred estimator for multi-tracer forecasts due to computational efficiency and stability.
Simultaneous Constraint Feasibility: It proves that $s_G(z)$ and $\beta$ can be constrained simultaneously without significant loss of precision, provided tomographic cross-correlations (between different redshift bins) are utilized.

4. Results

The Fisher forecasts yield the following quantitative improvements when combining galaxy surveys with HI IM:

Constraints on $\beta$ (Gravity Probe):
- The multi-tracer approach dramatically improves constraints on $\beta$ by factors of 25 to 50.
- Single Tracer (Euclid-like): $\sim 1\%$ uncertainty.
- Multi-Tracer (Euclid-like + SKAO): Uncertainty drops to $\sim 0.05\%$ .
- For DES-like and LSST-like surveys, uncertainty on $\beta$ drops from $\sim 20\%$ to $< 1\%$ when combined with HI surveys.
Constraints on $s_G(z)$ (Magnification Bias):
- Improvements are significant but less dramatic than for $\beta$ , ranging from marginal to factors of 2 to 8.
- The best result (Euclid + SKAO) achieves uncertainties as low as $\sim 0.07\%$ .
Degeneracy Breaking:
- The cross-correlations between different redshift bins (tomography) effectively break the local degeneracy between $s_G$ and $\beta$ that exists in auto-correlations.
- The addition of HI bins reduces the difference between separate and joint estimation to negligible levels.
Caveats:
- The effectiveness is limited by the overlapping sky fraction ( $f_{sky}$ ). For example, combining DES with SKAO yields slightly worse results for specific bins than DES with MeerKLASS because the smaller overlap with DES reduces the effective sky area, increasing shot noise despite SKAO's superior instrument specs.

5. Significance

Testing General Relativity: By constraining $\beta$ with sub-percent precision, this method offers a rigorous "null test" for General Relativity. A deviation from $\beta=1$ would indicate modified gravity or large anisotropic stress.
Access to Gravitational Potentials: Simultaneously constraining $s_G(z)$ allows for the isolation of the lensing convergence ( $\kappa$ ). Since $\kappa$ is an integral of $\Phi + \Psi$ , this provides a direct observational pathway to measure the sum of the gravitational potentials, a key quantity in testing gravity on cosmological scales.
Future Strategy: The paper establishes that the synergy between next-generation optical surveys (Euclid, LSST) and radio HI surveys (SKAO) is essential for extracting the full scientific potential of these datasets, moving beyond simple galaxy clustering to precision tests of fundamental physics.

In conclusion, the authors demonstrate that the multi-tracer combination of photometric and HI intensity mapping surveys enables high-precision measurements of both magnification bias and gravity parameters, opening a new window for testing the validity of General Relativity on the largest scales.