$\texttt{SBi3PCF:}$ Simulation-based inference with the integrated 3PCF

TL;DR

This work tackles extracting cosmological information from the integrated 3-point weak-lensing statistic i3PCF by adopting a simulation-based inference approach. It forward-models the cosmic shear field with the CosmoGridV1 N-body simulations, incorporating key systematics such as intrinsic alignment, baryonic feedback, photo-z uncertainty, shear calibration bias, and shape noise, and trains masked autoregressive flows to learn the data likelihood. The authors demonstrate that the joint 2PCF and i3PCF likelihood is non-Gaussian for large i3PCF scales, but that MOPED compression can restore Gaussianity and enable efficient inference, achieving a substantial median improvement of $63.8\%$ in the figure of merit for the $Ω_m−σ_8−w_0$ subspace on mock DES Y3-like data, with strong tightening on $σ_8$ and reduced projection effects on $w_0$. These results show the feasibility and value of SBI for real i3PCF analyses in wide-area surveys and establish a framework for applying i3PCF in future Stage-IV experiments like Euclid and LSST.

Abstract

We present $\texttt{SBi3PCF}$, a simulation-based inference (SBI) framework for analysing a higher-order weak lensing statistic, the integrated 3-point correlation function (i3PCF). Our approach forward-models the cosmic shear field using the $\texttt{CosmoGridV1}$ suite of N-body simulations, including a comprehensive set of systematic effects such as intrinsic alignment, baryonic feedback, photometric redshift uncertainty, shear calibration bias, and shape noise. Using this, we have produced a set of DES Y3-like synthetic measurements for 2-point shear correlation functions $ξ_{\pm}$ (2PCFs) and i3PCFs $ζ_{\pm}$ across 6 cosmological and 11 systematic parameters. Having validated these measurements against theoretical predictions and thoroughly examined for potential systematic biases, we have found that the impact of source galaxy clustering and reduced shear on the i3PCF is negligible for Stage-III surveys. Furthermore, we have tested the Gaussianity assumption for the likelihood of our data vector and found that while the sampling distribution of the 2PCF can be well approximated by a Gaussian function, the likelihood of the combined 2PCF + i3PCF data vector including filter sizes of $90'$ and larger can deviate from this assumption. Our SBI pipeline employs masked autoregressive flows to perform neural likelihood estimation and is validated to give statistically accurate posterior estimates. On mock data, we find that including the i3PCF yields a substantial $63.8\%$ median improvement in the figure of merit for $Ω_m - σ_8 - w_0$. These findings are consistent with previous works on the i3PCF and demonstrate that our SBI framework can achieve the accuracy and realism needed to analyse the i3PCF in wide-area weak lensing surveys.

Figures (21)

• Figure 1: The DES mask rotated to four non overlapping positions in the sky.
• Figure 2: Left: The redshift distribution of source galaxies for the 4 DES Y3 tomographic bins. The galaxy number densities are 1.476, 1.479, 1.484 and 1.461 per square arcminute respectively in these bins. Right: The lensing kernel for each bin.
• Figure 3: Comparison of the 2PCFs $\xi_+$ ($\triangle$) and $\xi_-$ ($\triangledown$) and measured in the CosmoGridV1 noiseless simulations at fiducial cosmology against theoretical predictions (grey). The simulation measurements are without shape noise, meaning the error bars reflect cosmic variance for a DES Y3-like survey footprint.
• Figure 4: Same as Figure \ref{['fig:2PCF_theory_val']} but for the i3PCFs $\zeta_+$ ($\triangle$) and $\zeta_-$ ($\triangledown$) with filter size $90'$.
• Figure 5: Histogram of $\chi^2$ values for the 16,000 fiducial measured full data vectors, without MOPED compression, comparing dark matter only simulations (red) with the expected $\chi^2$ distribution for a likelihood assumed to be Gaussian (black).