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

TL;DR

This work addresses unbiased inference of local-type primordial non-Gaussianity from the galaxy power spectrum by incorporating full relativistic and wide-separation corrections into the power-spectrum multipoles. It develops a consistent Cartesian framework to include integrated effects (lensing convergence, time delay, ISW) along with local relativistic projections and wide-separation corrections, and extends this to a full multi-tracer covariance; all results are implemented in CosmoWAP. The authors quantify biases that arise if these effects are neglected, show that luminosity-function uncertainties propagate into $f_{ m NL}$ constraints, and demonstrate that a bright-faint multi-tracer analysis can recover ~15–20% tighter constraints. They further provide analytic covariances for the multi-tracer case including wide-separation corrections, enabling robust parameter forecasts for upcoming surveys like Euclid, MegaMapper, and SKA2. The work offers practical tools and benchmarks for unbiased PNG analysis in next-generation large-scale structure surveys.

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$α$-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, $f_{\rm NL}$, 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 $f_{\rm NL}$. 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}.

Figures (20)

• Figure 1: Geometry of the local $2$-point function described by a single LOS, $\bm{d}$ where $t$ describes its choice along the vector $\bm{x}_{12}$.
• Figure 2: Monopole (top row) and the quadrupole (bottom row) of the power spectrum for each term over three different survey setups at set redshifts, with the standard Kaiser power spectrum shown in black (dashed).
• Figure 3: Imaginary dipole contribution for the bright-faint split cross-power spectrum of Euclid (left) ($F_c = 2\times10^{-16} \, [{\rm erg \, \,cm}^{-2} s^{-1}]$) and MegaMapper-like ($m_c=24$) (right) surveys.
• Figure 4: Ratio of power spectrum contributions when using a non-linear $P(k)$ (HMcode) modelling compared to using linear $P(k)$. The solid lines represent a $z=1$Euclid-like survey while the dashed lines represent a MegaMapper-like LBG survey at $z=3$. Other than the I× I term, all contributions are simply proportional to the ratio of the non-linear to the linear power spectra which is represented in black.
• Figure 5: PDF of the forecasted constraints on local $f_{\rm NL}$ for a fiducial value of $f_{\rm NL}=0$, after marginalising over $\alpha_{b_1}$, using a MCMC analysis (solid lines) and a Fisher analysis (dashed lines). Top panel considers the case where local relativistic effects and wide-separation corrections are ignored while the bottom panel considers the case where local relativistic, wide-separation and the integrated contributions are all neglected.