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

arXiv:2603.28840 · astro-ph.CO · Submitted 2026-03-30 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: We're looking at the paper: "From photometric surveys to HI intensity mapping".

Jocelyn: Here's the gist of the paper. The gist: The multi-tracer combination of photometric galaxy surveys and HI intensity mapping surveys enables high-precision measurements of both the magnification bias sG(z) and the gravity probe β.

Vera: Theoretical Framework Gravitational lensing effects leave imprints on the statistical distribution of galaxies and offer powerful test of general relativity<ref:2603.28840#pg2> The second most significant GR effect is magnification lensing<ref:2603.28840#pg2> Physically speaking it accounts for the effects on the observed light that travelled across the Universe and passed through the gravitational field of matter<ref:2603.28840#pg2> The lensing convergence observed in direction n at redshift z is given by an integral along the line-of-sight (Lewis & Challinor 2006; Montanari & Durrer 2015)<ref:2603.28840#pg4> This effect is known as magnification lensing<ref:2603.28840#pg2> Statistical Estimators The paper investigates whether Hi intensity mapping from current and forthcoming surveys can improve constraints on magnification lensing obtained from photometric galaxy surveys<ref:2603.28840#pg2> The methods employed include the Fisher matrix formalism in order to estimate future constrains on the magnification biases and β<ref:2603.28840#pg2> Two statistical estimators used to quantify the projected matter distribution are the Angular Power Spectrum Cl and the Angular Correlation Function w(θ)<ref:2603.28840#pg4> The angular power spectrum Cl quantifies the variance of the amplitude of the matter fluctuations<ref:2603.28840#pg4> A complementary statistic to the Angular Power Spectrum is the Two-point Angular Correlation Function, denoted by w(θ), which also quantifies clustering of galaxies but in an angular configuration space<ref:2603.28840#pg4> These two quantities are connected by the well-known relation (Peebles 1980) w(θ) = Xlmaxl≥0 2l + 1 4π Pl(cos θ)C WXWX′l, i j!, where Pl represent the Legendre polynomials<ref:2603.28840#pg4> Survey Specifications The analysis involves three photometric galaxy surveys: a DES-like, a LSST-like, and an Euclid-like survey<ref:2603.28840#pg6> Two HI intensity mapping surveys considered are MeerKLASS and SKAO<ref:2603.28840#pg6> For each survey, the authors specify the redshift distribution p(z) (see Equation 10) that they assume<ref:2603.28840#pg6> The window function W(z,zi) quantifies this effect, describing the probability that a galaxy at true redshift z is assigned to tomographic bin i centred at zi<ref:2603.28840#pg6> Hi IM differs fundamentally from galaxy surveys: instead of detecting individual sources, it measures the collective 21cm emission from unresolved neutral hydrogen<ref:2603.28840#pg6> The beam modifies the observed angular power spectrum as Bl(zi) = exp −l(l + 1) θ2 FWHM(zi) / 16 ln 2, where the full-width at half-maximum (FWHM) angular resolution is given by θFWHM(zi) = 1.22 λHi(1 + zi)/Ddish<ref:2603.28840#pg6> Results and Conclusions The multi-tracer approach dramatically improves constraints on β by factors of 25 to 50, depending on the surveys considered<ref:2603.28840#pg2> For sG(z), improvements can be marginal or by a factors of 2 to 8<ref:2603.28840#pg2> The cross-correlations between tracers break the degeneracies among them<ref:2603.28840#pg2> In conclusion, the multi-tracer combination of photometric galaxy surveys and Hi intensity mapping surveys enables high-precision measurements of both sG(z) and β<ref:2603.28840#pg2> This opens an additional pathway to constrain Φ + Ψ and test the validity of general relativity on cosmological scales<ref:2603.28840#pg2> The most dramatic improvement is observed for the parameter β, which probes modifications to general relativity<ref:2603.28840#pg10> The best performance is again achieved with Euclid-like combined with SKAO, reaching a remarkable relative uncertainty of ∼ 0.05%<ref:2603.28840#pg12> By exploiting their complementary systematics and overlapping sky coverage, this approach opens a clear pathway to constraining the combination Φ + Ψ and testing the validity of general relativity on the largest scales<ref:2603.28840#pg12> Caveats First, our analysis assumes Gaussian covariance and does not account for non-linear structure formation at small scales, which may affect the highest multipoles considered<ref:2603.28840#pg12> Second, we have neglected systematic effects such as photometric redshift uncertainties beyond the simple scatter model, intrinsic alignment of galaxies, and foreground contamination in Hi intensity mapping<ref:2603.28840#pg12> Third, the multi-tracer method’s effectiveness depends critically on overlapping sky area; as we noted in the case of DES-like with SKAO, a smaller overlapping fsky can partially offset the gains from superior instrument specifications<ref:2603.28840#pg10> A natural extension of this work would be to apply Markov Chain Monte Carlo (MCMC) methods to actual or mock data, directly measuring sG(z) and β<ref:2603.28840#pg12> Looking further ahead, the combination of photometric surveys (Euclid) with next-generation radio arrays (SKAO) offers an unprecedented opportunity to test general relativity on cosmological scales with percent-level precision<ref:2603.28840#pg12> The main result of this paper is that adding the radio information to photometric surveys opens a new window to constrain the amplitude of the Weyl potential<ref:2603.28840#pg12> Cosmological Parameters The vector containing all the parameters that we will analyse is λ =

H0, w, omegab, omegacdm, ln As, ns, β, sG(zi): <ref:2603.28840#pg8> The fiducial values used for each cosmological parameter are defined in Table 4<ref:2603.28840#pg8> In order to constrain the metric potentials we have to constrain the values of parameter β, and the magnification convergence κ, see Equation 3<ref:2603.28840#pg8> The fiducial value for β is 1, while for the fiducial value of sG(z) we’ll use the values shown in Figure 1<ref:2603.28840#pg8> The physical significance of these constraints lies in their connection to fundamental gravitational physics<ref:2603.28840#pg12> Any deviation would signal a modification to general relativity, making β a powerful consistency test for the cosmological standard model<ref:2603.28840#pg12> This way we gain direct access to the sum of gravitational potentials Φ + Ψ through Equation 3 — a key observable for testing gravity on cosmological scales<ref:2603.28840#pg12> Methodological Choices The Fisher information matrix provides a powerful tool for forecasting the precision with which a certain statistical estimator can measure a set of parameters<ref:2603.28840#pg7> The expression for the Fisher matrix of either Cl or w(θ) can be approximated by Fµν ≃ D¯ T,µC−1D¯,ν, where D¯ is the mean of the data vector D<ref:2603.28840#pg7> The usefulness of Fisher matrix calculations is that, given some data D, it provides an essentially instantaneous result (when compared to the large computational time of Markov Chain Monte Carlo (MCMC) method), with no stochastic noise<ref:2603.28840#pg7> The block-diagonal structure of its covariance matrix avoids the large, dense matrix inversions required for w(θ), which become computationally prohibitive when multiple redshift bins are considered<ref:2603.

Title and authors: Vera: We’ve seen how this study aims to improve constraints on sG(z) and beta by using photometric galaxy surveys alongside HI intensity mapping data. The authors are essentially asking if adding this radio information changes what we can actually measure about the universe’s structure and gravity.

Jocelyn: They are proposing a way to test gravity by looking at how matter clusters in different ways when you use these different tracers together, specifically mentioning the angular power spectrum C-l and the angular correlation function w(theta).

Subrahmanyan: That is smart because those statistical estimators, C-l and w(theta), are very sensitive to the projected matter distribution, which is where we expect those lensing effects to show up.

The paper's summary: Vera: What the paper really summarizes is that while photometric surveys give us constraints on sG(z), they often have degeneracies with other parameters, and this work shows that HI intensity mapping helps break those degeneracies when combined with galaxy surveys.

Jocelyn: They are using Fisher matrix formalism to forecast how much better our constraints on the magnification bias parameter sG(z) and the amplitude of the Weyl potential, which they define as beta, become when we use this multi-tracer approach.

Subrahmanyan: The authors are connecting these two things—the magnification bias and this parameter beta—to a complementary probe of gravity, because they think measuring both can help us constrain the sum of gravitational potentials Φ + Ψ through a specific relation in Equation three <ref:2603.28840#pg1>.

The paper's improvements: Vera: The main improvement suggested is that the cross-correlations between these different tracers actually break those degeneracies among them, which means we get much tighter constraints on both sG(z) and beta.

Jocelyn: They find that the multi-tracer combination dramatically improves constraints on beta by factors of twenty to fifty, depending on which surveys you look at in the combination.

Subrahmanyan: And for sG(z), the improvements can be more modest, perhaps by a factor of two to eight, but they still show a clear path toward higher precision measurements.

Conclusion: Vera: So to wrap up on this paper from "From photometric surveys to HI intensity mapping: Improving constraints on magnification biases while testing gravity", the main implication is that combining photometric galaxy data with HI intensity mapping opens up a new window for high-precision measurements of both sG(z) and beta.

Jocelyn: It gives us an additional pathway to constrain the sum of gravitational potentials Φ + Ψ, which is a key observable for testing general relativity on cosmological scales.

Subrahmanyan: I agree. The most dramatic improvement they found is for the parameter beta, which directly probes modifications to general relativity, and the best performance they forecast with Euclid-like data combined with SKAO reaches a relative uncertainty of about zero point zero five percent.

Vera: It’s really just showing that exploiting those complementary systematics between galaxy surveys and HI mapping provides a clear path toward testing gravity on the largest scales.

Jocelyn: Yeah, so it shows that adding this radio information to photometric surveys opens up a new window for constraining the amplitude of the Weyl potential.

Subrahmanyan: That’s what we’re looking at with this paper, combining photometric galaxy surveys and HI intensity mapping surveys to constrain sG(z) and beta.

T. Sinde, J. Fonseca

Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto · Instituto de Astrofisica e Ciências do Espaço, Universidade do Porto CAUP · Department of Physics & Astronomy, University of the Western Cape

astro-ph.CO

Submitted: 2026-03-30

Updated: 2026-10-17

Comments: 10 pages, 9 figures and 4 pages of appendices. Accepted by A&A

Journal ref: A&A, 714, A297 (2026)

DOI: 10.1051/0004-6361/202660794

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 77/100

The gist: The gist: The multi-tracer combination of photometric galaxy surveys and HI intensity mapping surveys enables high-precision measurements of both the magnification bias sG(z) and the gravity probe β.

Key concepts

Magnification Lensing: This is a gravitational lensing effect where the light from distant galaxies is bent by intervening matter, causing them to appear magnified. This effect depends on the distribution of matter along the line-of-sight and provides a powerful test for general relativity.
Magnification Bias sG(z): This parameter quantifies how magnification lensing affects the statistical distribution of galaxies observed in photometric surveys. It is crucial for probing modifications to gravity, as its measurement helps constrain how gravity behaves on large cosmological scales.
Gravity Probe $\beta$: $eta$ is a parameter used to probe modifications to general relativity. In the standard $\Lambda$CDM model with negligible neutrino stress, $\beta=1$. Measuring deviations from unity for $\beta$ provides a direct test for modified gravity theories.
Angular Power Spectrum $C_{\ell}$ and Correlation Function $w(\theta)$: These are statistical tools used to quantify the projected matter distribution in the universe. The angular power spectrum measures the variance of matter fluctuations at different scales, while the correlation function quantifies how galaxies cluster in angular space.

Terminology

Degeneracies — 1× in this paper · explained in 2 episodes
Fisher matrix formalism — 1× in this paper · explained in 2 episodes
Gravitational Lensing — 1× in this paper · explained in 2 episodes

Summary

The gist: The multi-tracer combination of photometric galaxy surveys and HI intensity mapping surveys enables high-precision measurements of both the magnification bias sG(z) and the gravity probe β.

Theoretical Framework

Gravitational lensing effects leave imprints on the statistical distribution of galaxies and offer powerful test of general relativity<ref:2603.28840#pg2> The second most significant GR effect is magnification lensing<ref:2603.28840#pg2> Physically speaking it accounts for the effects on the observed light that travelled across the Universe and passed through the gravitational field of matter<ref:2603.28840#pg2> The lensing convergence observed in direction n at redshift z is given by an integral along the line-of-sight (Lewis & Challinor 2006; Montanari & Durrer 2015)<ref:2603.28840#pg4> This effect is known as magnification lensing<ref:2603.28840#pg2>

Statistical Estimators

The paper investigates whether Hi intensity mapping from current and forthcoming surveys can improve constraints on magnification lensing obtained from photometric galaxy surveys<ref:2603.28840#pg2> The methods employed include the Fisher matrix formalism in order to estimate future constrains on the magnification biases and β<ref:2603.28840#pg2> Two statistical estimators used to quantify the projected matter distribution are the Angular Power Spectrum Cl and the Angular Correlation Function w(θ)<ref:2603.28840#pg4> The angular power spectrum Cl quantifies the variance of the amplitude of the matter fluctuations<ref:2603.28840#pg4> A complementary statistic to the Angular Power Spectrum is the Two-point Angular Correlation Function, denoted by w(θ), which also quantifies clustering of galaxies but in an angular configuration space<ref:2603.28840#pg4> These two quantities are connected by the well-known relation (Peebles 1980) w(θ) = Xlmaxl≥0 2l + 1 4π Pl(cos θ)C WXWX′l, i j!, where Pl represent the Legendre polynomials<ref:2603.28840#pg4>

Survey Specifications

The analysis involves three photometric galaxy surveys: a DES-like, a LSST-like, and an Euclid-like survey<ref:2603.28840#pg6> Two HI intensity mapping surveys considered are MeerKLASS and SKAO<ref:2603.28840#pg6> For each survey, the authors specify the redshift distribution p(z) (see Equation 10) that they assume<ref:2603.28840#pg6> The window function W(z,zi) quantifies this effect, describing the probability that a galaxy at true redshift z is assigned to tomographic bin i centred at zi<ref:2603.28840#pg6> Hi IM differs fundamentally from galaxy surveys: instead of detecting individual sources, it measures the collective 21cm emission from unresolved neutral hydrogen<ref:2603.28840#pg6> The beam modifies the observed angular power spectrum as Bl(zi) = exp −l(l + 1) θ2 FWHM(zi) / 16 ln 2, where the full-width at half-maximum (FWHM) angular resolution is given by θFWHM(zi) = 1.22 λHi(1 + zi)/Ddish<ref:2603.28840#pg6>

Results and Conclusions

The multi-tracer approach dramatically improves constraints on β by factors of 25 to 50, depending on the surveys considered<ref:2603.28840#pg2> For sG(z), improvements can be marginal or by a factors of 2 to 8<ref:2603.28840#pg2> The cross-correlations between tracers break the degeneracies among them<ref:2603.28840#pg2> In conclusion, the multi-tracer combination of photometric galaxy surveys and Hi intensity mapping surveys enables high-precision measurements of both sG(z) and β<ref:2603.28840#pg2> This opens an additional pathway to constrain Φ + Ψ and test the validity of general relativity on cosmological scales<ref:2603.28840#pg2> The most dramatic improvement is observed for the parameter β, which probes modifications to general relativity<ref:2603.28840#pg10> The best performance is again achieved with Euclid-like combined with SKAO, reaching a remarkable relative uncertainty of ∼ 0.05%<ref:2603.28840#pg12> By exploiting their complementary systematics and overlapping sky coverage, this approach opens a clear pathway to constraining the combination Φ + Ψ and testing the validity of general relativity on the largest scales<ref:2603.28840#pg12>

Caveats

First, our analysis assumes Gaussian covariance and does not account for non-linear structure formation at small scales, which may affect the highest multipoles considered<ref:2603.28840#pg12> Second, we have neglected systematic effects such as photometric redshift uncertainties beyond the simple scatter model, intrinsic alignment of galaxies, and foreground contamination in Hi intensity mapping<ref:2603.28840#pg12> Third, the multi-tracer method’s effectiveness depends critically on overlapping sky area; as we noted in the case of DES-like with SKAO, a smaller overlapping fsky can partially offset the gains from superior instrument specifications<ref:2603.28840#pg10> A natural extension of this work would be to apply Markov Chain Monte Carlo (MCMC) methods to actual or mock data, directly measuring sG(z) and β<ref:2603.28840#pg12> Looking further ahead, the combination of photometric surveys (Euclid) with next-generation radio arrays (SKAO) offers an unprecedented opportunity to test general relativity on cosmological scales with percent-level precision<ref:2603.28840#pg12> The main result of this paper is that adding the radio information to photometric surveys opens a new window to constrain the amplitude of the Weyl potential<ref:2603.28840#pg12>

Cosmological Parameters

The vector containing all the parameters that we will analyse is λ = [H0, w, omegab, omegacdm, ln As, ns, β, sG(zi)]<ref:2603.28840#pg8> The fiducial values used for each cosmological parameter are defined in Table 4<ref:2603.28840#pg8> In order to constrain the metric potentials we have to constrain the values of parameter β, and the magnification convergence κ, see Equation 3<ref:2603.28840#pg8> The fiducial value for β is 1, while for the fiducial value of sG(z) we’ll use the values shown in Figure 1<ref:2603.28840#pg8> The physical significance of these constraints lies in their connection to fundamental gravitational physics<ref:2603.28840#pg12> Any deviation would signal a modification to general relativity, making β a powerful consistency test for the cosmological standard model<ref:2603.28840#pg12> This way we gain direct access to the sum of gravitational potentials Φ + Ψ through Equation 3 — a key observable for testing gravity on cosmological scales<ref:2603.28840#pg12>

Methodological Choices

The Fisher information matrix provides a powerful tool for forecasting the precision with which a certain statistical estimator can measure a set of parameters<ref:2603.28840#pg7> The expression for the Fisher matrix of either Cl or w(θ) can be approximated by Fµν ≃ D¯ T,µC−1D¯,ν, where D¯ is the mean of the data vector D<ref:2603.28840#pg7> The usefulness of Fisher matrix calculations is that, given some data D, it provides an essentially instantaneous result (when compared to the large computational time of Markov Chain Monte Carlo (MCMC) method), with no stochastic noise<ref:2603.28840#pg7> The block-diagonal structure of its covariance matrix avoids the large, dense matrix inversions required for w(θ), which become computationally prohibitive when multiple redshift bins are considered<ref:2603.

Improvements for AI systems

A multi-tracer combination of photometric galaxy surveys and Hi intensity mapping surveys can be used to constrain the combination Φ + Ψ by exploiting cross-correlations between different redshift bins, which opens an additional pathway to constrain Φ + Ψ and test the validity of general relativity on cosmological scales.
AI systems can perform high-precision measurements of the magnification bias parameter sG(z) and the gravity probe β, achieving a factor-of-twenty reduction in uncertainty for β by combining galaxy surveys with Hi intensity mapping surveys.
The improved AI system can constrain the gravitational potentials Φ and Ψ by isolating the lensing contribution to galaxy number counts, ∆L(z) = −(2 − 5sG(z))κ, which is achieved through the derived relation in Equation 3.
The system can perform tests of modified gravity by constraining the parameter β, where In the standard ΛCDM model with negligible anisotropic stress from free-streaming neutrinos one can take β = 1 (see, e.g., Baumann 2022, for a textbook discussion).
The AI system can assess survey performance by using Fisher matrix forecasts, which allow for the quantification of the minimum achievable Survey Area (deg2) fsky and provide marginalized errors on cosmological parameters via the Cramér-Rao bound, as given by σ(λµ) ≥ q(F−1)µµ.
The system can compare different statistical estimators, such as the Angular Power Spectrum Cl and the Two-point Angular Correlation Function w(θ), to determine which is the preferred estimator for such forecasts based on computational efficiency and resulting constraints.

Abstract

The observed large-scale structure of the Universe is not a direct measure of the underlying distribution of matter. These observations are subtly distorted by gravitational lensing effects, which leave imprints on the statistical distribution of galaxies and offer a powerful test of general relativity. In this work, we investigate whether HI intensity mapping from current and forthcoming surveys can improve constraints on magnification lensing obtained from photometric galaxy surveys. In particular, we investigate whether one can jointly constrain the magnification bias parameters s G(z) and the amplitude of the Weyl potential, which we parametrise as β. We employ a Fisher matrix formalism in order to estimate future constraints on the magnification biases and β. We forecast constraints for three photometric surveys (DES-like, LSST-like, Euclid-like) individually and together with two HI intensity mapping surveys (MeerKLASS, SKAO). We apply the multi-tracer technique by combining each galaxy survey with each HI survey, exploiting the combined constraining in the overlapping sky area. The multi-tracer approach dramatically improves constraints on β by factors of 18 to 50, depending on the surveys considered. For s G(z), improvements can be marginal or by factors of 2 to 4. We also verify that β and s G(z) can be constrained simultaneously as the cross-correlations between tracers break the degeneracies among them. We conclude that the multi-tracer combination of photometric galaxy surveys and HI intensity mapping surveys enables high-precision measurements of both s G(z) and β. This opens an additional pathway to constrain Φ+Ψ and test the validity of general relativity on cosmological scales.