[Paper Review] KiDS-SBI: Simulation-based inference analysis of KiDS-1000 cosmic shear

Maximilian von Wietersheim-Kramsta, Kiyam Lin+5 more|arXiv (Cornell University)|Apr 23, 2024

Geophysics and Gravity Measurements7 citations

TL;DR

This paper performs a simulation-based inference analysis of KiDS-1000 cosmic shear using forward simulations with DELFI to infer cosmological parameters, yielding an S8 constraint and assessing systematics.

ABSTRACT

We present a simulation-based inference (SBI) cosmological analysis of cosmic shear two-point statistics from the fourth weak gravitational lensing data release of the ESO Kilo-Degree Survey (KiDS-1000). KiDS-SBI efficiently performs non-Limber projection of the matter power spectrum via Levin's method, and constructs log-normal random matter fields on the curved sky for arbitrary cosmologies, including effective prescriptions for intrinsic alignments and baryonic feedback. The forward model samples realistic galaxy positions and shapes based on the observational characteristics, incorporating shear measurement and redshift calibration uncertainties, as well as angular anisotropies due to variations in depth and point-spread function. To enable direct comparison with standard inference, we limit our analysis to pseudo-angular power spectra. The SBI is based on sequential neural likelihood estimation to infer the posterior distribution of spatially-flat $Λ$CDM cosmological parameters from 18,000 realisations. We infer a mean marginal of the growth of structure parameter $S_{8} \equiv σ_8 (Ω_\mathrm{m} / 0.3)^{0.5} = 0.731\pm 0.033$ ($68 \%$). We present a measure of goodness-of-fit for SBI and determine that the forward model fits the data well with a probability-to-exceed of $0.42$. For fixed cosmology, the learnt likelihood is approximately Gaussian, while constraints widen compared to a Gaussian likelihood analysis due to cosmology dependence in the covariance. Neglecting variable depth and anisotropies in the point spread function in the model can cause $S_{8}$ to be overestimated by ${\sim}5\%$. Our results are in agreement with previous analysis of KiDS-1000 and reinforce a $2.9 σ$ tension with constraints from cosmic microwave background measurements. This work highlights the importance of forward-modelling systematic effects in upcoming galaxy surveys.

Motivation & Objective

• Motivate a robust inference of cosmology from KiDS-1000 cosmic shear data.
• Apply simulation-based inference (SBI) with DELFI to learn the data likelihood without assuming a Gaussian form.
• Incorporate realistic forward-modeling of observational systematics including depth variations and PSF anisotropies.
• Compare SBI results to standard KiDS-1000 analyses and assess goodness-of-fit of the forward model.
• Quantify the impact of systematics on cosmological parameter constraints and assess tension with Planck CMB results.

Proposed method

• Use non-Limber projection to compute 2D angular power spectra from the 3D matter power spectrum.
• Construct log-normal random matter fields on curved sky via concentric shells and GLASS for forward modeling.
• Incorporate baryonic feedback via HMCode and intrinsic alignments into the forward model.
• Simulate realistic survey characteristics including depth variations, redshift calibration, and measurement uncertainties.
• Employ DELFI for neural density estimation to learn the implicit likelihood and perform posterior inference on, e.g., S8 in spatially-flat LCDM.
• Limit the data vector to pseudo-C_l (angular power spectra) to enable direct comparison with standard KiDS-1000 analyses.

Figure 1: Spatial map of the KiDS-1000 footprint. The top panel shows a Mollweide projection of the full KiDS-1000 footprint, while the two panels at the bottom show zoomed-in Cartesian projections of KiDS-North and KiDS-South fields, respectively.

Experimental results

Research questions

• RQ1 What is the posterior constraint on S8 from KiDS-1000 cosmic shear using SBI with realistic forward simulations?
• RQ2 How do depth variations and angular anisotropies affect the inferred cosmological parameters when propagated through SBI?
• RQ3 Is the learned SBI posterior approximately Gaussian for fixed cosmology, and how does the cosmology dependence of covariance affect constraints?
• RQ4 How well does the forward model fit the KiDS-1000 data (goodness-of-fit) and do systematics bias the cosmological results?
• RQ5 How do SBI results compare to traditional Gaussian-likelihood KiDS-1000 analyses and to CMB-based constraints?

Key findings

• SBI infers a mean marginal growth parameter S8 = 0.731 with ±0.033 (68%).
• The forward model provides a goodness-of-fit with a probability-to-exceed of 0.42, indicating an adequate fit to the data.
• For fixed cosmology, the learnt likelihood is approximately Gaussian, but constraints widen due to cosmology-dependent covariance.
• Neglecting depth variations and PSF anisotropies can bias S8 high by about 5%.
• Results are consistent with previous KiDS-1000 analyses and reinforce a 2.9-sigma tension with Planck CMB constraints on S8.

Figure 2: The redshift distributions of the five KiDS-1000 tomographic bins. The shaded areas show to limits of each tomographic bin, while the solid lines show the $n(z)$ of the source galaxies in each tomographic bin as a function of both redshift, $z$ , and comoving distance, $\chi$ (the latter i