Impacts of the physical data model on the forward inference of initial conditions from biased tracers

TL;DR

This paper examines how different components of a physical data model influence the Bayesian inference of initial cosmological conditions from biased tracers, highlighting the importance of bias and likelihood models for unbiased results.

Contribution

It provides a detailed analysis of the effects of tracer density, grid resolution, gravity, bias, and likelihood on initial condition inference, emphasizing the roles of bias and likelihood models.

Findings

Cross-correlation between true and inferred phases is weakly affected by model ingredients.

Amplitude bias depends strongly on bias and likelihood models.

Proper bias and likelihood modeling are crucial for unbiased cosmological inference.

Abstract

We investigate the impact of each ingredient in the employed physical data model on the Bayesian forward inference of initial conditions from biased tracers at the field level. Specifically, we use dark matter halos in a given cosmological simulation volume as tracers of the underlying matter density field. We study the effect of tracer density, grid resolution, gravity model, bias model and likelihood on the inferred initial conditions. We find that the cross-correlation coefficient between true and inferred phases reacts weakly to all ingredients above, and is well predicted by the theoretical expectation derived from a Gaussian model on a broad range of scales. The bias in the amplitude of the inferred initial conditions, on the other hand, depends strongly on the bias model and the likelihood. We conclude that the bias model and likelihood hold the key to an unbiased cosmological inference. Together they must keep the systematics -- which arise from the sub-grid physics that are marginalized over -- under control in order to obtain an unbiased inference.