pop-cosmos: Forward modeling KiDS-1000 redshift distributions using realistic galaxy populations

The accuracy of the cosmological constraints from Stage~IV galaxy surveys will be limited by how well the galaxy redshift distributions can be inferred. We have addressed this challenging problem for the Kilo-Degree Survey (KiDS) cosmic shear sample by developing a forward-modeling framework with two main ingredients: (1) the \texttt{pop-cosmos} generative model for the evolving galaxy population, calibrated on \textit{Spitzer} IRAC $\textit{Ch.\,1}<26$ galaxies from COSMOS2020; and (2) a data model for noise and selection, machine-learned from the SURFS-based KiDS-Legacy-Like Simulations (SKiLLS). Applying KiDS tomographic binning to our synthetic photometric data, we infer redshift distributions in each of five bins directly from the population and data models, bypassing the need for spectroscopic reweighting. Keeping the data model fixed, we compare results using two different galaxy population models: \texttt{pop-cosmos}; and \texttt{shark}, the semi-analytic galaxy formation model used in SKiLLS. In the first ($0.1<z<0.3$) and last ($0.9<z<1.2$) tomographic bins we find systematic differences in the mean redshifts of $\Delta z\sim0.05$-$0.1$, comparable to the reported uncertainties from spectroscopic reweighting methods. This work paves the way for accurate redshift distribution calibration for Stage~IV surveys directly through forward modeling, thus providing an independent cross-check on spectroscopic-based calibrations which avoids their selection biases and incompleteness. We will use the \texttt{pop-cosmos} redshift distributions in an upcoming full KiDS cosmology reanalysis.