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.
Highlights
Standard approaches in cosmological inference and reconstruction from LSS data, often rely on either modeling of n-point functions of galaxies [e.g. 1–4] or reversing the evolution of matter fluctuations by moving mass particles or galaxies backward [e.g. 5–8]
We summarize the connection between these ingredients of the physical data model in Figure 1, where we have generalized “galaxy” to “biased tracer”, partially due to the fact that our results are obtained using DM halos in N-body simulations, and because most of our results and arguments apply to all generic biased tracers
We use DM main halos identified in N-body simulations, for which the true initial conditions are known, as physical biased tracers
Summary
Standard approaches in cosmological inference and reconstruction from LSS data, often rely on either modeling of n-point functions of galaxies [e.g. 1–4] or reversing the evolution of matter fluctuations by moving mass particles or galaxies backward (reconstruction hereafter) [e.g. 5–8]. We are interested in the aforementioned more direct route: forward modeling the matter and galaxy clustering directly at the field-level [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24] This alternative path circumvents the difficult and cumbersome problem of how to accurately predict and compute the higher n-point functions (plus their covariances) from theory [25,26,27,28,29] and data [1, 30], respectively, and, in principle, accesses all information available in the three-dimensional data field above the smoothing scale, regardless of its Gaussianity. This final piece attempts to model the scatter in the deterministic matter-galaxy bias relation, i.e. the difference between the deterministic and observed galaxy fields, in the form of a conditional probability [18,19,20,21]
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