Modeling Redshift Uncertainties in Roman Weak Lensing Cosmology

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 $\Omega_m$, 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 $\Omega_m$, and can achieve comparable performance with fewer parameters than the nine tomographic-bin mean-shift model.