Self-consistent ray-traced weak-lensing convergence in screened modified gravity: modified clustering and modified lensing with physically derived screening

Stage IV weak-lensing surveys require predictions of the convergence power spectrum in modified gravity (MG) that are accurate on both linear and non-linear scales. Pantiri et al. (2026) made a first step by ray-tracing FLAMINGO simulation maps with a phenomenological modification of the lensing equation (a time-dependent function $\Sigma_{\rm mg}$ with hand-imposed, halo- or overdensity-based screening), while keeping matter clustering governed by general relativity (GR). They find percent-level enhancements of the convergence spectrum and a $>5\sigma$ bias in the inferred $\sigma_8$ , showing modified lensing matters at Stage IV precision. The open problem is the full, self-consistent case: convergence maps in which both the clustering ( $\mu_{\rm mg}\neq 1$ , produced by MG-native simulations) and the lensing relation ( $\Sigma_{\rm mg}\neq 1$ ) are non-trivially modified, with screening determined by the actual environmental density field and the non-linear dynamics of the scalar field rather than by hand-imposed prescriptions, together with the resulting impact on inferred cosmological parameters. As of August 2026 no published work treats this case; the authors list it as future work.

Background

Weak gravitational lensing — the coherent distortion of distant galaxy shapes by the tidal field of intervening matter — is a primary cosmological probe, and Stage IV surveys (Euclid, Rubin Observatory/LSST, Roman) will measure its convergence maps (the projected matter density weighted by lensing geometry, customarily summarized by the angular power spectrum $C_\ell$ — a function of angular multipole $\ell$ — of the convergence field) with percent-level precision. This demands accurate modeling on both linear and non-linear scales. Extensions of the standard $\Lambda$ CDM cosmology (cold dark matter plus a cosmological constant) in which gravity deviates from general relativity (GR) on large scales — modified gravity (MG) models — generically alter both how matter clusters and how light is deflected. Viable MG models must be equipped with a screening mechanism (e.g. chameleon, Vainshtein, symmetron, or k-mouflage), which suppresses the deviations from GR in high-density, well-tested environments such as the Solar System and galaxy halos, and which therefore makes the modifications non-linear and environment-dependent on cosmological scales. A standard phenomenological description (Zhang et al. 2007; Pogosian & Silvestri 2016) captures the two effects by two functions of scale factor $a$ and wavenumber $k$ : the Poisson equation for the Newtonian potential $\Psi$ acquires an effective clustering modification $\mu_{\rm mg}$ , $\nabla^2\Psi = 4\pi G\,\mu_{\rm mg}(a,k)\,a^2\rho_m\delta_m$ , while the Poisson equation for the lensing potential $\Phi_{\rm W}=(\Phi+\Psi)/2$ (the combination of the metric potentials that deflects light) acquires a separate factor $\Sigma_{\rm mg}$ , $\nabla^2\Phi_{\rm W} = 4\pi G\,\Sigma_{\rm mg}(a,k)\,a^2\rho_m\delta_m$ . GR is recovered when $\mu_{\rm mg}=\Sigma_{\rm mg}=1$ ; a mismatch between them corresponds to a gravitational slip between the two potentials. Most non-linear MG studies to date (e.g. the MGLenS suite of Harnois-Déraps et al. 2023, built on the FORGE and BRIDGE suites of $f(R)$ -gravity (gravity theories in which the gravitational action is generalized to a function of the Ricci scalar) and normal-branch DGP (the stable branch of the Dvali–Gabadadze–Porrati braneworld gravity model) $N$ -body simulations, and the convergence maps of Hoyland et al. 2025 generated with the COLA method (COmoving Lagrangian Acceleration, a fast approximate $N$ -body technique)) simulate modified clustering but compute the lensing signal with the standard GR prescription — a good approximation for $f(R)$ and DGP, where the lensing modification is tiny. Conversely, ray-traced lensing with a genuinely modified lensing equation has been explored only rarely, notably by Barreira et al. (2017) for normal-branch DGP and a phenomenological variant with a directly modified lensing potential, using stacked convergence profiles around under- and overdense lines of sight. Pantiri et al. (2026) bridged part of this gap: using the backward ray-tracing pipeline of Broxterman et al. (2024) applied to the FLAMINGO hydrodynamical simulation light cones (which assume GR), they multiplied the lensing-source term by $\Sigma_{\rm mg}(a)=1+\Sigma_0\,\Omega_\Lambda(a)/\Omega_{\Lambda,0}$ with a value $\Sigma_0=0.044$ motivated by current constraints from DESI (the Dark Energy Spectroscopic Instrument survey), and imposed screening by hand with two prescriptions — reverting to GR lensing inside the virial radii of halos above a mass threshold, or inside pixels above an overdensity threshold. They found that the convergence power spectrum is enhanced by about 5% at $\ell\approx100$ (decreasing towards small scales where screening operates), that the two screening prescriptions differ on small scales, and that fitting these MG spectra with a standard GR $\Lambda$ CDM model biases $\sigma_8$ (the present-day amplitude of matter fluctuations) by more than $5\sigma$ — a larger effect than baryonic feedback for their setup. However, this analysis is a limiting case: the density maps still cluster as in GR ( $\mu_{\rm mg}=1$ ), the screening is a hand-imposed mask with known artifacts (the screened spectra fail to converge to the unscreened one on large scales, which in the updated journal-version discussion the authors explain as a consequence of the masking prescription itself — the screened regions are a biased selection of the sky, so within this implementation there is no one-to-one correspondence between screened regions and small scales — rather than of the GR density maps), and the halo-based method is only usable on hydrodynamical runs. Realistic MG models modify clustering and lensing simultaneously, with screening that depends on the full environmental density field and on the non-linear dynamics of the underlying scalar field.

Problem Statement

Construct the full, self-consistent case that Pantiri et al. (2026) deliberately left open: predictions of the weak-lensing convergence power spectrum (via ray tracing through simulated light cones) in screened modified gravity in which both the clustering of matter is non-trivially modified ( $\mu_{\rm mg}\neq 1$ , requiring simulations that themselves evolve structure under the modified theory rather than under GR) and the lensing equation is non-trivially modified ( $\Sigma_{\rm mg}\neq 1$ ), with the screening that suppresses these modifications in dense environments determined by the full environmental density field and the non-linear dynamics of the underlying scalar field, instead of the hand-imposed halo-radius or overdensity-threshold masks used in the source analysis. The single overarching objective is a self-consistent Stage-IV-level prediction of the modified-lensing observable and its observational consequences for modifications that are sizeable at Stage-IV precision — of the order of the percent-level convergence-spectrum enhancement produced by the DESI-motivated $\Sigma_0=0.044$ in the source analysis, or the comparable level predicted by any screened modified-gravity theory whose convergence-spectrum modification is of that order — rather than for a model observationally indistinguishable from $\Lambda$ CDM, jointly supported by the following linked components: (i) MG-native density maps (e.g. modified-gravity runs of the FLAMINGO suite) ray-traced with the modified lensing prescription, replacing the hand-imposed phenomenological screening masks that were applied to GR density maps; and (ii) characterization of the resulting convergence power spectra and of the bias in inferred $\Lambda$ CDM parameters (e.g. $\sigma_8$ , $\Omega_{\rm m}$ ). In this case the clustering modification and the lensing modification are simultaneously active and mutually consistent (the same underlying theory producing the growth, the lensing, and the environmental screening).

References

Pantiri, M., Schaller, M., Silvestri, A., Broxterman, J. C., & Schaye, J. (2026). Ray-traced weak lensing convergence in screened modified gravity theories. Monthly Notices of the Royal Astronomical Society, 551. DOI: 10.1093/mnras/stag1523; arXiv:2604.08393. https://doi.org/10.1093/mnras/stag1523
Barreira, A., Bose, S., Li, B., & Llinares, C. (2017). Weak lensing by galaxy troughs with modified gravity. Journal of Cosmology and Astroparticle Physics, 2017(02), 031. DOI: 10.1088/1475-7516/2017/02/031; arXiv:1605.08436. https://doi.org/10.1088/1475-7516/2017/02/031
Harnois-Déraps, J., Hernandez-Aguayo, C., Cuesta-Lazaro, C., Arnold, C., Li, B., Davies, C. T., & Cai, Y.-C. (2023). MGLenS: modified gravity weak lensing simulations for emulation-based cosmological inference. Monthly Notices of the Royal Astronomical Society, 525, 6336–6358. DOI: 10.1093/mnras/stad2700; arXiv:2211.05779. https://doi.org/10.1093/mnras/stad2700
Hoyland, S., Winther, H. A., Saadeh, D., Koyama, K., & Izard, A. (2025). Fast generation of weak lensing maps in modified gravity with COLA. Monthly Notices of the Royal Astronomical Society, 541, 3167–3183. DOI: 10.1093/mnras/staf1071. https://doi.org/10.1093/mnras/staf1071
Zhang, P., Liguori, M., Bean, R., & Dodelson, S. (2007). Probing gravity at cosmological scales by measurements which test the relationship between gravitational lensing and matter overdensity. Physical Review Letters, 99, 141302. DOI: 10.1103/PhysRevLett.99.141302. https://doi.org/10.1103/PhysRevLett.99.141302
Pogosian, L., & Silvestri, A. (2016). What can cosmology tell us about gravity? Constraining Horndeski gravity with $\Sigma$ and $\mu$ . Physical Review D, 94, 104014. DOI: 10.1103/PhysRevD.94.104014. https://doi.org/10.1103/PhysRevD.94.104014
Broxterman, J. C., Schaller, M., Schaye, J., Hoekstra, H., Kuijken, K., Helly, J. C., Kugel, R., Braspenning, J., Elbers, W., Frenk, C. S., Kwan, J., McCarthy, I. G., Salcido, J., van Daalen, M. P., & Vandenbroucke, B. (2024). The FLAMINGO project: baryonic impact on weak gravitational lensing convergence peak counts. Monthly Notices of the Royal Astronomical Society, 529(3), 2309–2326. DOI: 10.1093/mnras/stae698; arXiv:2312.08450. https://doi.org/10.1093/mnras/stae698