Modeling Redshift Uncertainties in Roman Weak Lensing Cosmology

TL;DR

This work tackles redshift-distribution uncertainties in Roman Space Telescope weak lensing by implementing an optimized PCA-based marginalization of the full redshift distribution shape within the CoCoA pipeline, validated against Cardinal realizations. Compared to the traditional mean-shift approach, the PCA method can reduce cosmological biases, particularly under mild-to-strong miscalibration, often achieving comparable performance with fewer nuisance parameters. The study demonstrates that a weighted PCA, informed by the response of the cosmic-shear observables, provides robust bias mitigation across a diverse set of Roman observing scenarios, though some deep-field configurations (e.g., W2-D3) pose challenges. The results support PCA-based redshift marginalization as a flexible, scalable approach for next-generation surveys, with potential extensions to dynamical dark energy models and broader multi-probe analyses.

Abstract

Cosmological constraints using weak gravitational lensing measurements from the Roman Space Telescope will require a powerful method for modelling uncertainties in the galaxy redshift distribution. In this work, we use an optimized version of the principal component analysis (PCA) to model uncertainties in the full shape of the redshift distributions, a method proposed by \cite{pca_method} and recently used in the Dark Energy Survey Y6 analysis. Here, we implement this new approach within the Roman High Latitude Imaging Survey (HLIS) Cosmology Project Infrastructure Team (PIT) pipeline, namely Cobaya-Cosmolike Joint Architecture (\texttt{CoCoA}). To validate the PCA in mitigating biases on cosmological parameters, $S_8$ and $Ω_m$, we use a set of redshift distributions from \texttt{Cardinal} generated for a variety of Roman configurations. Overall, when the simulated cosmic shear data vector is not strongly miscalibrated relative to the fiducial one, both the mean-shift and the PCA-based approaches produce consistent cosmological constraints when marginalizing over nuisance parameters. For mild to strong miscalibration, including additional PCs progressively mitigates biases in $S_8$ and $Ω_m$, and can achieve comparable performance with fewer parameters than the nine tomographic-bin mean-shift model.

Figures (13)

• Figure 1: Estimated redshift distributions for different wide- and deep-tier specifications. Lighter lines display a small illustrative subsample of 100 (out of 1 million) realizations, with their spread reflecting the uncertainty in their exact shape, whereas the darker dashed lines show the mean redshift distribution computed over all 1 million realizations. Each row pairs a fixed wide tier (W1-W3) with a deep tier (D1-D4), except for the combination W3-D3.
• Figure 2: Quantities derived from the Roman scenario W1-D1. Top: mean redshift distribution (dark dashed lines) obtained from the ensemble of 1 million realizations, along with 100 individual realizations (faint lines). Bottom: difference between the mean redshift distribution and the individual realizations per tomographic bin.
• Figure 3: Singular value decomposition of the difference matrix $\mathbf{\Delta}$ for the $N_\text{sim}=10^6$ realizations for the redshift distributions. The unitary matrix $\mathbf{D}$ holds the left singular vectors and $\tilde{\mathbf{U}}^T$ contains the right singular vectors, while $\mathbf{\Sigma}$ possesses the singular values; the upper $414\times414$ block contains the positive real singular values $\sigma_1,\ldots,\sigma_{414}$ in decreasing order, and the dashed square indicates that all remaining entries are zero.
• Figure 4: Two-dimensional projection of the ensemble of the SVD application to the redshift distributions of Roman scenario W1-D1. Gray points represent draws from a Gaussian distribution with mean zero and a covariance matrix. The correlations between dimensions are captured by the covariance of the difference vectors $\Delta_i$. The arrows indicate the first ($\mathbf{PC}_1$) and second ($\mathbf{PC}_2$) principal components.
• Figure 5: The first four and the last four PC modes, as function of the redshift, across the nine tomographic redshift bins for the Roman scenario W1-D1.