[Paper Review] Towards a full $w$CDM map-based analysis for weak lensing surveys

D. Zürcher, Janis Fluri+4 more|arXiv (Cornell University)|Jun 3, 2022

Galaxies: Formation, Evolution, Phenomena5 citations

TL;DR

This paper develops a full wCDM map-based analysis framework for weak lensing surveys, extending forward modeling to include higher-order statistics like peak and minima counts, Minkowski functionals, and wavelet filtering. It finds that combining angular power spectra, peak counts, and Minkowski functionals with Starlet filtering yields the most constraining, cost-effective constraints for stage 4 surveys, even after stringent scale cuts due to unmodeled baryons.

ABSTRACT

The next generation of weak lensing surveys will measure the matter distribution of the local Universe with unprecedented precision, allowing the resolution of non-Gaussian features of the convergence field. This encourages the use of higher-order mass-map statistics for cosmological parameter inference. We extend the forward-modelling based methodology introduced in a previous forecast paper to match these new requirements. We provide multiple forecasts for the wCDM parameter constraints that can be expected from stage 3 and 4 weak lensing surveys. We consider different survey setups, summary statistics and mass map filters including wavelets. We take into account the shear bias, photometric redshift uncertainties and intrinsic alignment. The impact of baryons is investigated and the necessary scale cuts are applied. We compare the angular power spectrum analysis to peak and minima counts as well as Minkowski functionals of the mass maps. We find a preference for Starlet over Gaussian filters. Our results suggest that using a survey setup with 10 instead of 5 tomographic redshift bins is beneficial. Adding cross-tomographic information improves the constraints on cosmology and especially on galaxy intrinsic alignment for all statistics. In terms of constraining power, we find the angular power spectrum and the peak counts to be equally matched for stage 4 surveys, followed by minima counts and the Minkowski functionals. Combining different summary statistics significantly improves the constraints and compensates the stringent scale cuts. We identify the most `cost-effective' combination to be the angular power spectrum, peak counts and Minkowski functionals following Starlet filtering.

Motivation & Objective

• To develop a comprehensive, forward-modeling-based analysis pipeline for weak lensing surveys that incorporates higher-order mass map statistics beyond the angular power spectrum.
• To evaluate the constraining power of various summary statistics—angular power spectrum, peak counts, minima counts, Minkowski functionals—under realistic survey conditions including shear bias, photometric redshift errors, and intrinsic alignment.
• To assess the impact of baryonic physics on statistical constraints and derive necessary scale cuts for dark-matter-only simulations in stage 4 surveys.
• To identify the most cost-effective combination of summary statistics that maximizes cosmological constraint power while remaining robust to unmodeled baryonic effects.
• To compare the performance of different mass map filters (Gaussian vs. Starlet) and tomographic binning schemes (5 vs. 10 redshift bins) in cosmological inference.

Proposed method

• Adopts a forward-modelling approach using simulated mass maps from COSMOGRID dark-matter-only simulations to predict observable statistics under the wCDM cosmological model.
• Applies multiple mass map filters—Gaussian and Starlet wavelets—prior to statistical analysis to enhance sensitivity to non-Gaussian features.
• Employs a suite of summary statistics: angular power spectrum, peak and minima counts, and Minkowski functionals, to extract cosmological information from the projected matter distribution.
• Incorporates observational systematics including shear bias, photometric redshift uncertainties, and non-linear intrinsic alignment (NLA) effects in the likelihood framework.
• Applies scale cuts based on baryonic feedback effects to ensure robustness, derived from comparing dark-matter-only and hydrodynamical simulations.
• Combines multiple statistics using a joint likelihood approach to extract complementary information and improve overall cosmological constraints.

Experimental results

Research questions

• RQ1 How do different summary statistics (angular power spectrum, peak counts, minima counts, Minkowski functionals) compare in constraining wCDM parameters under realistic stage 4 survey conditions?
• RQ2 What is the optimal choice of mass map filter (Gaussian vs. Starlet) for maximizing cosmological constraint power in map-based weak lensing analysis?
• RQ3 How does increasing the number of tomographic redshift bins from 5 to 10 affect cosmological constraints and the recovery of intrinsic alignment parameters?
• RQ4 To what extent can combining multiple summary statistics mitigate the loss of constraining power due to stringent scale cuts imposed by unmodeled baryonic physics?
• RQ5 Which combination of statistics and filters yields the most cost-effective and robust cosmological constraints for future stage 4 weak lensing surveys?

Key findings

• Starlet filtering outperforms Gaussian filtering in constraining power, particularly when combined with other statistics, due to its multiscale sensitivity to non-Gaussian features.
• Using 10 instead of 5 tomographic redshift bins significantly improves cosmological constraints, especially for intrinsic alignment parameters.
• Cross-tomographic information enhances constraints across all statistics, with the greatest improvement seen in intrinsic alignment and S8 parameter estimation.
• For stage 4 surveys, the angular power spectrum and peak counts are equally constraining, followed by minima counts and Minkowski functionals.
• The combination of angular power spectrum, peak counts, and Minkowski functionals with Starlet filtering provides the most cost-effective and robust constraint set, compensating for scale cuts due to baryonic physics.
• Even after applying conservative scale cuts to mitigate baryonic effects, the combined statistic approach yields competitive constraints and mildly constrains prior-dominated parameters like ns, Ωb, H0, and η.