Unclustered tracers remain unclustered: the lack of primordial non-Gaussianity response of bias-zero tracers
Constraining primordial non-Gaussianities (PNG) is one of the main goals of new-generation large-scale galaxy surveys. It had been proposed that unclustered tracers (with bias $b_1=0$) could be optimal for PNG studies, and that these could be found by selecting galaxies in bins of their local density. Here, we test this hypothesis in state-of-the-art simulations from the PNG-UNITsim suite with local $f_{\rm NL}=100$ and $f_{\rm NL}=-20$. We consider different parent tracer catalogues: all halos together, halos in large mass bins, and HOD models for LRGs and QSO. We then classify these tracers by their local density ($\delta_{t,R}$) and measure the linear bias ($b_1$) and PNG-response ($b_\phi$). Most $\delta_{t,R}$ bins show a PNG-response compatible with $b_\phi=0$ for all halos or the low-mass bin (log$M<11$). For high-mass halos (log$M>$12), QSO or LRG, we recover a trend closer to the universality relation ($b_\phi = 2 \delta_{\rm crit}(b_1-1)$) for $b_1>1$, but the $b_\phi(b_1)$ curve flattens to 0 below $\vert b_1\lvert<1$. Hence, we find $b_\phi\approx0$ for all bias-zero tracers considered. The complex $\delta_{t,R}$-based selection causes their clustering to strongly deviate from simple assumptions, namely the universality relation and Poisson shot noise, hindering their capability to constrain PNG.