[Paper Review] Map-based cosmology inference with lognormal cosmic shear maps

Supranta S. Boruah, Eduardo Rozo+1 more|arXiv (Cornell University)|Apr 27, 2022

Statistical Methods and Inference4 citations

TL;DR

This paper introduces a map-based cosmology inference framework that models the cosmic convergence field as a lognormal random field conditioned on weak lensing shear data, enabling joint inference of cosmological parameters and mass maps. It achieves a 30% improvement in cosmological constraints on σ₈–Ωₘ compared to standard two-point function methods by capturing non-Gaussian features and accounting for cross-bin correlations.

ABSTRACT

Most cosmic shear analyses to date have relied on summary statistics (e.g. $ξ_+$ and $ξ_-$). These types of analyses are necessarily sub-optimal, as the use of summary statistics is lossy. In this paper, we forward-model the convergence field of the Universe as a lognormal random field conditioned on the observed shear data. This new map-based inference framework enables us to recover the joint posterior of the cosmological parameters and the convergence field of the Universe. Our analysis properly accounts for the covariance in the mass maps across tomographic bins, which significantly improves the fidelity of the maps relative to single-bin reconstructions. We verify that applying our inference pipeline to Gaussian random fields recovers posteriors that are in excellent agreement with their analytical counterparts. At the resolution of our maps -- and to the extent that the convergence field can be described by the lognormal model -- our map posteriors allow us to reconstruct \it all m summary statistics (including non-Gaussian statistics). We forecast that a map-based inference analysis of LSST-Y10 data can improve cosmological constraints in the $σ_8$--$Ω_{ m m}$ plane by $\approx 30\%$ relative to the currently standard cosmic shear analysis. This improvement happens almost entirely along the $S_8=σ_8Ω_{ m m}^{1/2}$ directions, meaning map-based inference fails to significantly improve constraints on $S_8$.

Motivation & Objective

• To develop a map-based inference framework that captures non-Gaussian cosmological information from weak lensing shear data more effectively than traditional two-point statistics.
• To address limitations in existing map-based methods, including coarse resolution, single-bin reconstruction, and fixed cosmological parameters.
• To enable joint inference of cosmological parameters and the 2D convergence field using a Bayesian forward-modelling approach with a lognormal prior.
• To improve mass map fidelity by properly accounting for covariance across tomographic redshift bins.
• To forecast the cosmological constraint gains of this method on upcoming LSST-Y10 data.

Proposed method

• The method employs a Bayesian forward-modelling framework that samples the 2D convergence field under a multivariate lognormal prior, conditioned on observed cosmic shear data.
• It jointly infers cosmological parameters and the convergence field by solving the posterior distribution using Markov Chain Monte Carlo (MCMC) sampling.
• The framework accounts for cross-correlations between tomographic redshift bins, significantly improving map reconstruction fidelity over single-bin approaches.
• It uses a Gaussian approximation to the likelihood of shear data given the convergence field, enabling efficient sampling of the joint posterior.
• The method is validated on Gaussian random fields, showing excellent agreement with analytical posteriors.
• The approach is extended to handle realistic LSST-Y10-like simulations, incorporating realistic source redshift distributions and noise models.

Experimental results

Research questions

• RQ1 Can a map-based inference framework that models the convergence field as a lognormal random field recover cosmological parameters and mass maps with higher fidelity than two-point statistics?
• RQ2 How does accounting for cross-bin covariance in tomographic shear data improve mass map reconstruction and cosmological constraints?
• RQ3 To what extent does the lognormal prior capture non-Gaussian features such as peaks and voids in the convergence field?
• RQ4 What is the gain in cosmological constraint precision when using map-based inference versus standard power spectrum-based analysis on LSST-Y10 data?
• RQ5 How does the method perform under realistic survey conditions, including shape noise and photometric redshift uncertainties?

Key findings

• The map-based inference framework recovers cosmological posteriors that are in excellent agreement with analytical expectations when tested on Gaussian random fields.
• The method successfully reconstructs all summary statistics, including non-Gaussian ones like peak and void counts, under the lognormal model.
• Accounting for cross-bin covariance in tomographic bins leads to significantly improved mass map fidelity compared to single-bin reconstructions.
• On LSST-Y10-like simulations, the method improves cosmological constraints in the σ₈–Ωₘ plane by approximately 30% compared to standard two-point function analysis.
• The improvement is almost entirely along the S₈ = σ₈Ωₘ¹ᐟ² direction, indicating limited gains in constraining S₈.
• The method remains robust to prior misspecification only when the lognormal model holds; small-scale non-Gaussianity may require more advanced priors like normalizing flows or GANs.