Field-Level Simulation-Based Inference of Large-Scale Structure

Abstract

Constraining the cosmological parameters that govern the ΛCDM model of the universe represents one of the central tasks in the current era of precision cosmol- ogy. Among the variety of data used to constrain these parameters, the large-scale structure (LSS) of the universe presents a particularly attractive method of infer- ence for the mass density, Ωm, and the mass fluctuation amplitude, σ8. Histori- cally, this inference has relied on a Bayesian approach using theoretical models of galaxy clustering from perturbation theory (PT). However, these analyses suffer from both an inability to model non-linearities in the LSS at small scales as well as difficulties in handling observational systematics. Simulation-based inference (SBI), which leverages machine learning to approximate likelihood-free posteriors from high-fidelity forward models of the LSS, has already proven capable of mit- igating both of these problems. Nonetheless, previous applications of SBI have relied on compressing the density field to the power spectrum, which limits their ability to capture non-Gaussian features present in the LSS. In the present paper, we explore the first-ever application of SBI to cosmological parameter inference from the LSS directly at field-level. Specifically, we employ the SimBIG forward modelling pipeline to generate a realistic catalogue of mock forward models of the Baryon Oscillation Spectroscopic Survey at varying cosmologies. Then, we use a Convolutional Neural Network with stochastic weight averaging to compress the density fields directly to the cosmological parameters. Finally, we use Neural Pos- terior Estimation to approximate posteriors over these parameters. We validate our analysis pipeline using coverage tests across a variety of out-of-distribution test datasets. Having demonstrated that our pipeline is conservative, we infer Ωm = 0.318 ± 0.036 and σ8 = 0.784 ± 0.049 on the BOSS CMASS data. Ulti- mately, our inferred posteriors on Ωm and σ8 are both consistent with and tighter than those achieved by both PT and SBI analyses that rely on first compressing the galaxy distribution to the power spectrum. The methods presented in this paper lay a valuable foundation for future analyses on larger boxes and smaller scales with both current SDSS data, as well as future DESI data. This thesis is ac- companied by an academic publication titled SimBIG: Field-level simulation-based inference of large-scale structure as part of the SimBIG collaboration.