Forecasting local Primordial Non-Gaussianities from UNIONS Lyman-Break Galaxies and Planck CMB lensing

Local Primordial non-Gaussianities (PNGs), characterized by $f_{\rm NL}^{\rm loc}$, provide a powerful window into the physics of inflation. Cross-correlating high-redshift tracer samples with the CMB lensing potential offers a particularly robust probe of PNGs, mitigating imaging systematics that typically affect large-scale measurements from tracer auto-spectra. In this context, UNIONS enables the selection of $u$-dropout high-redshift Lyman-Break Galaxies (LBGs). We perform a MCMC-based forecast to estimate the uncertainties on $f_{\rm NL}^{\rm loc}$ and on a galaxy bias parameter, which captures our uncertainty in the tracer bias. From the angular cross-power spectrum between LBGs and Planck CMB lensing, we forecast $\sigma(f_{\rm NL}^{\rm loc})=34$ for an idealized photometric sample of $r<24.3$ LBGs selected with a Random Forest classification algorithm from UNIONS-like $ugriz$ imaging, with a resulting surface density of $1,100$ deg$^{-2}$. This precision can be improved to $\sigma(f_{\rm NL}^{\rm loc})=20$ after spectroscopic follow-up with DESI, during its next phase starting in 2029, DESI-II. We test a more realistic $u$-dropout LBG selection using early UNIONS data, which yields a denser sample of $r<24.2$ objects at $1,400$ deg$^{-2}$. From this sample, covering a larger footprint and expected to have a higher large-scale galaxy bias, we forecast $\sigma(f_{\rm NL}^{\rm loc})=20$, with similar precision achievable after DESI spectroscopic follow-up. In addition, we perform preliminary validation of the redshift distribution using the clustering-redshift method with DESI DR1 data, confirming the calibration from deep, small-area photometric fields. However, accounting for uncertainties in the clustering-redshift distribution significantly degrades the $f_{\rm NL}^{\rm loc}$ constraining power.