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

TL;DR

This paper develops a relativistic framework for analyzing the galaxy power spectrum multipoles to accurately measure primordial non-Gaussianity, addressing biases from relativistic effects and luminosity function uncertainties.

Contribution

It introduces a comprehensive relativistic correction framework for the galaxy power spectrum multipoles and demonstrates mitigation strategies using multi-tracer analysis.

Findings

Ignoring relativistic effects biases f_NL measurements by up to 20 sigma.

Including these effects reduces bias and improves measurement accuracy.

Multi-tracer analysis enhances constraints on primordial non-Gaussianity.

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$\alpha$-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, $f_{\rm NL}$, of around $ 3\,\sigma$ and $ 20 \, \sigma$ respectively. When we include these corrections, the uncertainty in our knowledge of the luminosity function leads to further uncertainty in our measurement of $f_{\rm NL}$. 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 $f_{\rm NL}$. 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}.