Priors on red galaxy stochasticity from hybrid effective field theory

Abstract

We investigate the stochastic properties of typical red galaxy samples in a controlled numerical environment. We use Halo Occupation Distribution (HOD) modelling to create mock realizations of three separate bright red galaxy samples consistent with datasets used for clustering and lensing analyses in modern galaxy surveys. Second-order Hybrid Effective Field Theory (HEFT) is used as a field-level forward model to describe the full statistical distribution of these tracer samples, and their stochastic power spectra are directly measured and compared to the Poisson shot-noise prediction. While all of the galaxy samples we consider are hosted within haloes with sub-Poisson stochasticity, we observe that the galaxy samples themselves possess stochasticities that range from sub-Poisson to super-Poisson, in agreement with predictions from the halo model. As an application of our methodology, we place priors on the expected degree of non-Poisson stochasticity in cosmological analyses using such samples. We expect these priors will be useful in reducing the complexity of the full parameter space for future analyses using second-order Lagrangian bias models. More generally, the techniques outlined here present the first application of hybrid EFT methods to characterize models of the galaxy–halo connection at the field level, revealing new connections between once-disparate modelling frameworks.

Cosmological analysis of three-dimensional BOSS galaxy clustering and Planck CMB lensing cross correlations via Lagrangian perturbation theory

“…[24] with two exceptions: we have narrowed the counterterm α n priors in the view that they are in any case sufficiently well constrained by the data that the priors are uninformative, and that they should represent only modest corrections to linear theory on scales where perturbation theory is valid. We have also updated the prior on the isotropic stochastic term R 3 h for the higher-redshift sample to better reflect the effective number density of the z3, where n−1 ≈ 6000 h −3 Mpc 3 , such that the priors on R 3 h in both z1 and z3 reflect the latest studies on stochasticity in BOSS-like galaxies [109]. Adopting these new priors shift our constraints on σ 8 by roughly 0.2 σ, with all other parameters essentially unaffected, compared to ref.…”

“…In figure 14 we show the fractional change in including higher order bias operators in the model for C gκ for a DESI-like sample of galaxies cross-correlated with Planck and SO CMB lensing. The bias parameters used are derived from the field-level inference of [109] for a DESI-like HOD. The binning adopted uses bins ∆ ≈ 3 √ , and each error bar should be thought of as an independent data point.…”

Accurate predictions from small boxes: variance suppression via the Zel'dovich approximation

“…For every box we estimate a value of b 1 using the field-level bias estimator of ref. [35] at k max = 0.2 hMpc −1 , but the variance reduction obtained is insensitive to the exact value of b 1 adopted as long as the analytic and grid-based ZA predictions use consistent values 12 . The results from applying our linearly biased control variate are shown in both panels of Fig.…”

“…Their combination leads to a powerful field-level description of the building blocks of structure formation. Recent applications of Hybrid EFT include: constructing emulators of clustering and lensing which are accurate to k 0.6 hMpc −1 [30][31][32], modelling higher order statistics beyond the power spectrum [33], and characterizing the tracer-matter connection of simulated samples of galaxies [34,35].…”

Statistics of biased tracers in variance-suppressed simulations

“…Notice that in this expression b 1 must be equal to 1, and is merely a bookkeeping parameter; in the next sections we will refer to the bias parameter denoted here by b δ as b L 1 , that is, the linear Lagrangian bias. Recent work [6][7][8][9][10][16][17][18] has shown that one can use this modeling and perform the advection using the nonlinear displacement field predicted by simulations to obtain accurate predictions for the power spectra of biased tracers at highly nonlinear scales. We call this general procedure "hybrid Lagrangian bias expansion".…”