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, therefore requiring 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 \textit{Euclid}-like H$\hat{I}\pm$-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, $f_{\mathrm{NL}}$, of around $3\ddot{I}ƒ$ and $20\ddot{I}ƒ$ respectively. When we include these corrections, the uncertainty in our knowledge of the luminosity function leads to further uncertainty in our measurement of $f_{\mathrm{NL}}$. In this work, 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, which provides a $15$--$20\%$ improvement on the forecasted constraints of local type $f_{\mathrm{NL}}$. 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 \textit{Python} code \textsc{CosmoWAP}.

53 pages, 22 figures. Code available at: https://github.com/craddis1/CosmoWAP. Accepted to JCAP