Weak-lensing minima — the local minima of smoothed convergence maps, probing underdense regions — were shown by Coulton, Liu, McCarthy & Osato (2020) to add non-Gaussian cosmological information complementary to peak counts and the power spectrum, with combined minima+peaks forecasts improving LSST-like constraints on the neutrino mass sum, matter density, and fluctuation amplitude by 44%, 11%, and 63% over the power spectrum alone. That analysis, however, modeled baryonic feedback with a single linear interpolation parameter assumed cosmology-independent, omitted observational systematics, and used a Gaussian likelihood. The subsequent literature isolates the surviving open core: can minima and combined peak–minimum counts deliver unbiased Stage-IV constraints when baryonic feedback and intrinsic alignments are jointly modeled and marginalized — rather than avoided by scale cuts — with the baryon effects captured by a more general parameterization than the single linear interpolation parameter, and do the forecast gains survive this marginalization?

Background

In weak gravitational lensing, the correlated distortions of distant galaxy images trace the projected matter density; the field is commonly summarized by the convergence κ\kappa, a dimensionless projected mass density. Because the late-time density field is non-Gaussian, two-point statistics such as the shear power spectrum capture only part of the available information. Map-level statistics extract the rest: peak counts (local maxima of the smoothed κ\kappa map, tracing massive halos and clusters) have long been studied, and Coulton, Liu, McCarthy & Osato (2020) introduced lensing minima — local minima of the smoothed map, tracing underdense regions — as a complementary statistic. In practice, maps are smoothed (e.g., with a 2 arcmin Gaussian filter) to suppress shape noise, the noise from the intrinsic ellipticities of source galaxies, and extrema are binned by signal-to-noise into count histograms. Coulton et al. built a Gaussian-process emulator — an interpolator of the statistic across a grid of simulated cosmologies — using the MassiveNuS suite, 101 N-body simulations with varying neutrino mass, matter density, and fluctuation amplitude, and inferred parameters with a Gaussian likelihood on the binned counts. Baryonic processes (gas cooling, star formation, and especially AGN feedback that ejects gas from halos) redistribute matter on precisely the nonlinear small scales probed by extrema; Coulton et al. modeled this by linearly interpolating between dark-matter-only predictions and hydrodynamical predictions from the BAHAMAS suite (a set of cosmological hydrodynamical simulations calibrated to reproduce observed cluster gas fractions) and the Osato et al. (2015) runs, via a single parameter AbaryonA_{\text{baryon}} assumed independent of cosmology. They found that ignoring baryons biases peak-count inference by about 4σ4\sigma but minima by only about 0.5σ0.5\sigma, and that marginalizing AbaryonA_{\text{baryon}} restores unbiased cosmology at little cost in precision. The authors themselves flagged the limitations that define the present problem: a simple linear model was used to capture the baryonic effects, so more accurate modeling of baryons would be beneficial, for instance via more flexible parametrizations (e.g., principal-component-style approaches); and intrinsic alignments (the tidal correlation of galaxy shapes with the density field, which contaminates the lensing signal since it is not a gravitational shear), photometric-redshift uncertainties, and multiplicative shear calibration biases were not modeled. Stage-IV surveys (Rubin Observatory LSST, Euclid, Roman) will reach the precision where all of these effects matter. Related developments in the field: simulation-based inference (SBI) replaces the Gaussian likelihood by learning the mapping from simulations to posteriors; wavelet (starlet) multi-scale filtering generalizes single-scale smoothing; and separate baryon-mitigation frameworks exist for two-point statistics.

Problem Statement

Establish whether weak-lensing minima and combined peak–minimum count statistics can deliver unbiased cosmological constraints at Stage-IV survey precision (LSST/Euclid/Roman) when baryonic feedback and the observational systematics are jointly modeled rather than avoided. The overarching objective is an inference for these statistics in which: (a) baryonic feedback is modeled with a more general and more accurate parametrization — going beyond the single linear interpolation parameter AbaryonA_{\text{baryon}} between dark-matter-only and one hydrodynamical prediction (e.g., principal-component-style approaches, as in the source work's future-work list); and (b) intrinsic alignments — shown to significantly boost high-significance minima — plus photometric-redshift uncertainties and multiplicative shear biases are modeled and their impact on minimum and combined counts quantified, with the baryonic and alignment nuisances marginalized over in the inference. The decisive scientific question: after joint marginalization over the baryonic and alignment nuisances, do minima and combined peak–minimum counts remain unbiased — residual parameter shifts small compared with the statistical uncertainties — and does the forecast gain over the power-spectrum-only analysis (44%, 11%, and 63% on ∑mν\sum m_\nu, Ωm\Omega_m, and AsA_s in the source work) survive this marginalization, or is it substantially degraded as baryon-marginalization studies of other weak-lensing statistics (a 2–5× degradation) would suggest?

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