Primordial Non-Gaussianity from Biased Tracers: Likelihood Analysis of Real-Space Power Spectrum and Bispectrum

TL;DR

This paper assesses how galaxy clustering measurements, specifically the power spectrum and bispectrum, can improve constraints on primordial non-Gaussianity, emphasizing the importance of accurate modeling and priors in analysis.

Contribution

It introduces a comprehensive likelihood analysis combining real-space power spectrum and bispectrum, accounting for bias parameters and systematics, to enhance constraints on primordial non-Gaussianity.

Findings

Combining power spectrum and bispectrum improves constraints on $f_{NL}$ by over a factor of 5.

Strong priors on bias parameters can tighten constraints but may introduce systematic shifts.

Assuming Poisson noise without marginalizing can lead to significant biases in $f_{NL}$ estimation.

Abstract

Upcoming galaxy redshift surveys promise to significantly improve current limits on primordial non-Gaussianity (PNG) through measurements of 2- and 3-point correlation functions in Fourier space. However, realizing the full potential of this dataset is contingent upon having both accurate theoretical models and optimized analysis methods. Focusing on the local model of PNG, parameterized by $f_{\rm NL}$, we perform a Monte-Carlo Markov Chain analysis to confront perturbation theory predictions of the halo power spectrum and bispectrum in real space against a suite of N-body simulations. We model the halo bispectrum at tree-level, including all contributions linear and quadratic in $f_{\rm NL}$, and the halo power spectrum at 1-loop, including tree-level terms up to quadratic order in $f_{\rm NL}$ and all loops induced by local PNG linear in $f_{\rm NL}$. Keeping the cosmological parameters fixed, we examine the effect of informative priors on the linear non-Gaussian bias parameter on the statistical inference of $f_{\rm NL}$. A conservative analysisof the combined power spectrum and bispectrum, in which only loose priors are imposed and all parameters are marginalized over, can improve the constraint on $f_{\rm NL}$ by more than a factor of 5 relative to the power spectrum-only measurement. Imposing a strong prior on $b_\phi$, or assuming bias relations for both $b_\phi$ and $b_{\phi\delta}$ (motivated by a universal mass function assumption), improves the constraints further by a factor of few. In this case, however, we find a significant systematic shift in the inferred value of $f_{\rm NL}$ if the same range of wavenumber is used. Likewise, a Poisson noise assumption can lead to significant systematics, and it is thus essential to leave all the stochastic amplitudes free.