Primordial non-Gaussianity systematics from redshift mismatch with SPHEREx

The ability to differentiate between different models of inflation through the imprint of primordial non-Gaussianity (PNG) requires stringent constraints on the local PNG parameter $f_{\text{NL}}^{\text{loc}}$. Upcoming data from the large scale structure surveys like \textit{Euclid}, Vera C. Rubin Observatory, and the Spectro-Photometer for the History of the Universe, Epoch of Reionization, and Ices Explorer (SPHEREx) will be instrumental in advancing our understanding of the inflationary epoch. In this context, we present forecasts on PNG with tomographic angular power spectra derived from simulations of SPHEREx. We put forward the effects of redshift bin mismatch of galaxies as a significant source of systematic uncertainty in the estimation of both $f_{\text{NL}}^{\text{loc}}$ and galaxy linear halo bias. We simulate $500$ SPHEREx-like galaxy density fields, and divide the galaxies into redshift bins assuming Gaussian photometric redshift errors. We show that the misclassification of galaxies in redshift bins can result in strong apparent tensions on $f_{\text{NL}}^{\text{loc}}$ up to $\sim 3-6\sigma$ and up to $\sim 9-12\sigma$ on galaxy bias. To address this, we propose a scattering matrix formalism that mitigates bin mismatch of galaxies and enables unbiased estimation of cosmological parameters from tomographic angular clustering measurements.