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

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 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 NL , and the halo power spectrum at 1-loop, including tree-level terms up to quadratic order in f NL and all loops induced by local PNG linear in f 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 NL . An entirely agnostic, conservative analysis of the combined power spectrum and bispectrum, in which all parameters are marginalized over, can improve the constraint on f NL by more than a factor of 5 relative to the power spectrum-only measurement. Imposing a strong prior on b φ , or assuming bias relations for both b φ and b φδ (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 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.

Predictions for local PNG bias in the galaxy power spectrum and bispectrum and the consequences for $f_{\rm NL}$ constraints

“…A we validate this strategy to estimate b φδ by applying it (with the appropriate modifications described there) to estimate the second-order bias parameter b 2 , whose values can be compared with known results in the literature. We note before proceeding that the b φδ parameter can also be estimated by fitting perturbation theory models to the bispectrum measured from simulations with local PNG initial conditions [45]. This requires however very large simulation volumes (in fact still currently out of reach for selfconsistent galaxy formation simulations) in order to measure the bispectrum precisely on large-scales where the effects of f nl dominate.…”

“…For the multitracer part of the data vector, we split this galaxy sample into a low-and a high-stellarmass subsamples, with M * ∈ 5 × 10 We assume Poissonian statistics for the fiducial power spectrum and bispectrum of the noise terms, i.e., P = 1/n g , P δ = b 1 /(2n g ) and B = 1/n 2 g (but note that we sample these in our constraints too; see Ref. [45] for the importance of k-dependent corrections to the shot noise in f nl constraints).…”

“…The adoption of a noiseless data vector is naturally idealized, but which we note is the most adequate choice for our purpose here to study the impact of galaxy bias uncertainties; see also Ref. [45], who takes halo power spectra and bispectra measurements from simulations as the data vector, and so the assessment of the true impact of bias uncertainties gets complicated by the limitations of the theory model to describe the simulation measurements. We consider 42 k-bins between k min = π/V 1/3 s and k max = 0.2 h/Mpc (in intervals of k min up to 0.01h/Mpc and of 10 × k min beyond that).…”

“…[16,43] discussed how the b φ (b 1 ) relation of recently-merged objects differs also from the universality prediction; we will return to these findings below when we reproduce some with our numerical results. The impact that uncertainties on the b φ (b 1 ) relation have on the resulting f nl constraints is only now beginning to be explored [44,45], but it is crucial that these investigations are made robust and mature since they will ultimately directly impact the final constraints on f nl . Beyond leading-order, the contributions at next-to-leading-order (NLO) are 2 δ g (x, z)…”

The local PNG bias of neutral Hydrogen, ${\rm H_I}$

“…Since the observational signatures of f nl are effectively degenerate with the bias parameters, a solid understanding of the latter is critical to obtain the best possible constraints on local PNG from large-scale structure data (see Refs. [32][33][34] for recent discussions). However, as the bias parameters effectively describe how the long-wavelength environment impacts the H I distribution, they depend on the complicated interplay between gravity, reionization, star formation and stellar/black hole feedback, and are thus extremely challenging to predict theoretically.…”