Optimal constraints on Primordial non-Gaussianity with the eBOSS DR16 quasars in Fourier space

We present constraints on the amplitude of local Primordial Non-Gaussianities (PNG), fNL, using the quasar sample in the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 (DR16). We analyze the power spectrum monopole, testing for the presence of scale-dependent galaxy bias induced by local PNG. Our analysis makes use of optimal redshift weights that maximize the response of the quasar sample to the possible presence of non-zero PNG. We find -4 < fNL < 27 at 68% confidence level, which is among the strongest bounds with Large Scale Structure data. The optimal analysis reduces the error bar by ~10% compared to the standard one, but this improvement is lower than the one expected from previous forecasts. In addition, the larger volume of this dataset, when compared to previous releases of the eBOSS quasar catalog, does not always correspond to a reduction of the final uncertainty on local PNG. This could suggest the presence of still unknown systematic effects in the data. If the quasars have a lower response to local PNG, our optimal constraint becomes -23 < fNL < 21 at 68%, with an improvement of 30% over standard analyses. We also show how to use the optimal weights to put data-driven priors on the sample's response to local PNG.