Non-Gaussian Galaxy Stochasticity and the Noise-Field Formulation

TL;DR

This work reframes galaxy stochasticity in the EFT of large-scale structure as local nonlinear couplings to a single Gaussian noise field, introducing a noise-field formulation that yields a normalized, field-level likelihood. By proving equivalence with the general partition-function approach order-by-order, it provides a practical route for field-level inference that includes non-Gaussian and density-dependent stochasticity. The authors implement this in LEFTfield and demonstrate first field-level cosmology inferences on dark matter halos, finding a consistent $ frac{\sigma_8}{\sigma_{8, m fid}}$ and a physically reasonable noise amplitude that avoids the prior pathologies of the formal likelihood. The approach enables robust incorporation of stochastic EFT contributions for parameter inference, albeit with increased computational cost due to sampling two coupled fields. Overall, the paper advances EFT-based field-level modeling by delivering a scalable, normalized framework for stochastic galaxy bias with non-Gaussianity, and shows promising initial results for cosmological inferences.

Abstract

We revisit the stochastic, or noise, contributions to the galaxy density field within the effective field theory (EFT) of large-scale structure. Starting from the general, all-order expression of the EFT partition function, we elucidate how the stochastic contributions can be described by local nonlinear couplings of a single Gaussian noise field. We introduce an alternative formulation of the partition function in terms of such a noise field, and derive the corresponding field-level likelihood for biased tracers. This noise-field formulation can capture the complete set of stochastic contributions to the galaxy density at the field level in a normalized, positive-definite probability density which is suitable for numerical sampling. We illustrate this by presenting the first results of EFT-based field-level inference with non-Gaussian and density-dependent stochasticity on dark matter halos using LEFTfield.

Figures (2)

• Figure 1: Trace plot (left panel) and normalized autocorrelation function $\rho(n)=\xi(n)/\xi(0)$ for the parameter $\alpha \equiv \sigma_8/\sigma_{8,\rm fid}$ in four independent FLI chains for the "SNG" rest-frame dark matter halo sample from FBISBI. The autocorrelation for each chain is estimated after removing a burn-in phase of 100,000 samples. The thick line in the right panel shows the mean autocorrelation across the four chains, while the thin lines indicate the error on the mean estimated from the sample variance across correlation functions.
• Figure 2: Trace plot (left panel) and normalized autocorrelation function $\rho(n)=\xi(n)/\xi(0)$ for the noise-amplitude parameter $c_\epsilon$ for the same chains as in Fig. \ref{['fig:alphatrace']} (blue shades, labeled A--D). In the trace plot we also show the results of two chains using the same noise-field formulation but with non-Gaussian and density-dependent noise turned off ($b^{\{1\}}_\delta = 0 = b^{\{2\}}_{\mathbb{1}}$; maroon shades). These latter chains show that $c_\epsilon$ drifts to its lower limit $0.05$, a trend previously found for Gaussian likelihoods in nguyen/etal:2020FBISBIakitsu/etal:2025.