Bispectrum constraints on Primordial non-Gaussianities with the eBOSS DR16 quasars

Abstract: We present constraints on $f_{\rm NL}$, the parameter quantifying the amplitude of local Primordial Non-Gaussianities (PNG), from a combined analysis of the tree-level power spectrum and bispectrum of Data Release $16$ (DR16) of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) quasar sample. In our analysis, we use the power spectrum measured with the optimal redshift weights that maximize the local PNG information together with the bispectrum estimated with the standard Feldman-Kaiser-Peacock weights. In the modeling, we incorporate the global and radial integral constraint corrections both in the power spectrum and in the bispectrum, for which we observe that only the radial integral constraint correction has a significant impact. Our constraints read $-6 < f_{\rm NL} < 20$ at $68\%$ confidence level and improve by $\sim 16\%$ over the previous power spectrum analysis of the same dataset. We observe the same improvement over the power spectrum analysis when the quasar response to PNG is lower. In this case, we find $-23 < f_{\rm NL} < 14$ at $68\%$ confidence level. Our findings are consistent with the Fisher matrix expectations.