Impact of redshift distribution uncertainties on Lyman-break galaxy cosmological parameter inference

A significant number of Lyman-break galaxies (LBGs) with redshifts $3 \lesssim z \lesssim 5$ are expected to be observed by the upcoming Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). This will enable us to probe the Universe at higher redshifts than is currently possible with cosmological galaxy clustering and weak lensing surveys. However, accurate inference of cosmological parameters requires precise knowledge of the redshift distributions of selected galaxies, where the number of faint objects expected from LSST alone will make spectroscopic based methods of determining these distributions extremely challenging. To overcome this difficulty, it may be possible to leverage the information in the large volume of photometric data alone to precisely infer these distributions. This could be facilitated using forward models, where in this paper we use stellar population synthesis (SPS) to estimate uncertainties on LBG redshift distributions for a 10yr LSST (LSSTY10) survey. We characterize some of the modelling uncertainties inherent to SPS by introducing a flexible parametrization of the galaxy population prior, informed by observations of the galaxy stellar mass function (GSMF) and cosmic star formation rate density (CSFRD). These uncertainties are subsequently marginalised over and propagated to cosmological constraints in a Fisher forecast, leveraging galaxy clustering and lensing of the cosmic microwave background (CMB). Assuming a known dust attenuation model for LBGs, we forecast constraints on the σ₈ parameter comparable to Planck CMB constraints.