Unbiased analysis of primordial non-Gaussianity: the multipoles of the full relativistic power spectrum

Abstract A 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 H α -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 3 σ and 20 σ 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 .