Optimizing primordial non-Gaussianity measurements from galaxy surveys

Galaxy clustering data from current and upcoming large scale structure surveys can provide strong constraints on primordial non-Gaussianity through the scale-dependent halo bias. To fully exploit the information from galaxy surveys, optimal analysis methods need to be developed and applied to the data. Since the halo bias is sensitive to local non-Gaussianity predominately at large scales, the volume of a given survey is crucial. Consequently, for such analyses we do not want to split into redshift bins, which would lead to information loss due to edge effects, but instead analyse the full sample. We present an optimal technique to directly constrain local non-Gaussianity parametrised by $f_\mathrm{NL}^\mathrm{loc}$, from galaxy clustering by applying redshift weights to the galaxies. We derive a set of weights to optimally measure the amplitude of local non-Gaussianity, $f_\mathrm{NL}^\mathrm{loc}$, discuss the redshift weighted power spectrum estimators, outline the implementation procedure and test our weighting scheme against Lognormal catalogs for two different surveys: the quasar sample of the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) and the emission line galaxy sample of the Dark Energy Spectroscopic Instrument (DESI) survey. We find an improvement of 30 percent for eBOSS and 6 percent for DESI compared to the standard Feldman, Kaiser $\&$ Peacock weights, although these predictions are sensitive to the bias model assumed.