Guedezounme, SêclokaClarkson, ChrisCamera, StefanoJolicoeur, SheeanMaartens, Roy2026-07-132026-07-132026Addis, C., Guedezounme, S.L., Hammond, J., Clarkson, C., Montano, F., Camera, S., Jolicoeur, S. and Maartens, R., 2026. Unbiased analysis of primordial non-Gaussianity: the multipoles of the full relativistic power spectrum. Journal of Cosmology and Astroparticle Physics, 2026(06), p.039.https://doi.org/10.1088/1475-7516/2026/06/039https://hdl.handle.net/10566/24915A major goal of ongoing and future cosmological surveys of the large-scale structure is to measure local type primordial non-Gaussianity in the galaxy power spectrum through the scale-dependent bias. General relativistic effects have been shown to be degenerate with this measurement and therefore one needs to consider a non-Newtonian approach. In this work, we develop a consistent framework to compute integrated effects, including lensing convergence, time delay, and integrated Sachs-Wolfe, along with the local relativistic projection and wide-separation corrections in the multipoles of the power spectrum. We show that, for a Euclid-like Hα-line galaxy survey and a MegaMapper-like Lyman-break galaxy survey, ignoring these effects leads to a bias on the best fit measurement of the amplitude of primordial non-Gaussianity, f NL, of around 3σ and 20σ respectively. When we include these corrections, the uncertainty in our knowledge of the luminosity function leads to further uncertainty in our measurement of f NL. However, we show that this degeneracy can be partly mitigated by using a bright-faint multi-tracer analysis, where the observed galaxy sample is subdivided into two separate populations based on luminosity. This provides a 15–20% improvement on the forecasted constraints of local type f NL. In addition, we present a novel calculation of the full multi-tracer covariance with the inclusion of wide-separation corrections. All of these results are implemented in the Python code CosmoWAP.encosmological parameters from LSSpower spectrumredshift surveysprimordial non-Gaussianitymulti-tracer covarianceArticle