Primordial non-Gaussianities and zero bias tracers of the Large Scale Structure

We develop a new method to constraint primordial non-Gaussianities of the local kind using unclustered tracers of the Large Scale Structure. We show that in the limit of low noise, zero bias tracers yield large improvement over standard methods, mostly due to vanishing sampling variance. We propose a simple technique to construct such a tracer, using environmental information obtained from the original sample, and validate our method with N-body simulations. Our results indicate that $\sigma_{f_{\mathrm{NL}}^{\mathrm{loc}}}\simeq1$ can be reached using only information on a single tracer of sufficiently high number density.