EFTofLSS meets simulation-based inference: $\sigma_8$ from biased tracers

TL;DR

This paper demonstrates how simulation-based inference can be used to estimate the cosmological parameter sigma_8 from biased tracers in large-scale structure, bypassing the need for explicit likelihood functions.

Contribution

It introduces a method combining EFT-based forward modeling with neural density estimation for sigma_8 inference from power spectrum and bispectrum data.

Findings

Covariance form impacts inference more than non-Gaussianity at certain scales.

Simulation-based inference matches traditional methods when covariance is accurately modeled.

The approach is effective for scales up to 0.2h/Mpc.

Abstract

Cosmological inferences typically rely on explicit expressions for the likelihood and covariance of the data vector, which normally consists of a set of summary statistics. However, in the case of nonlinear large-scale structure, exact expressions for either likelihood or covariance are unknown, and even approximate expressions can become very cumbersome, depending on the scales and summary statistics considered. Simulation-based inference (SBI), in contrast, does not require an explicit form for the likelihood but only a prior and a simulator, thereby naturally circumventing these issues. In this paper, we explore how this technique can be used to infer $\sigma_8$ from a Lagrangian effective field theory (EFT) based forward model for biased tracers. The power spectrum and bispectrum are used as summary statistics to obtain the posterior of the cosmological, bias and noise parameters via neural density estimation. We compare full simulation-based inference with cases where the data vector is drawn from a Gaussian likelihood with sample and analytical covariances. We conclude that, for $k_{\text{max}}=0.1h\text{Mpc}^{-1}$ and $0.2h\text{Mpc}^{-1}$, the form of the covariance is more important than the non-Gaussianity of the likelihood, although this conclusion is expected to depend on the cosmological parameter inferred, the summary statistics considered and range of scales probed.