Learning to Concentrate: Multi-tracer Forecasts on Local Primordial Non-Gaussianity with Machine-Learned Bias

Local primordial non-Gaussianity (LPNG) is predicted by many non-minimal models of inflation, and creates a scale-dependent contribution to the power spectrum of large-scale structure (LSS) tracers, whose amplitude is characterized by $b_{\phi}$. Knowledge of $b_{\phi}$ for the observed tracer population is therefore crucial for learning about inflation from LSS. Recently, it has been shown that the relationship between linear bias $b_1$ and $b_{\phi}$ for simulated halos exhibits significant secondary dependence on halo concentration. We leverage this fact to forecast multi-tracer constraints on $f_{NL}^{\mathrm{loc}}$. We train a machine learning model on observable properties of simulated Illustris-TNG galaxies to predict $b_{\phi}$ for samples constructed to approximate DESI emission line galaxies (ELGs) and luminous red galaxies (LRGs). We find $\sigma(f_{NL}^{\mathrm{loc}}) = 2.3$, and $\sigma(f_{NL}^{\mathrm{loc}}) = 3.7$, respectively. These forecasted errors are roughly factors of 3, and 35\% improvements over the single-tracer case for each sample, respectively. When considering both ELGs and LRGs in their overlap region, we forecast $\sigma(f_{NL}^{\mathrm{loc}}) = 1.5$ is attainable with our learned model, more than a factor of 3 improvement over the single-tracer case, while the ideal split by $b_{\phi}$ could reach $\sigma(f_{NL}^{\mathrm{loc}}) <1$. We also perform multi-tracer forecasts for upcoming spectroscopic surveys targeting LPNG (MegaMapper, SPHEREx) and show that splitting tracer samples by $b_{\phi}$ can lead to an order-of-magnitude reduction in projected $\sigma(f_{NL}^{\mathrm{loc}})$ for these surveys.