# Source clustering impact on Euclid weak lensing high-order statistics

In the coming years, the Euclid mission will provide measurements of the shapes and positions of billions of galaxies with unprecedented precision. As the light from the background galaxies travels through the Universe, it is deflected by the gravity of cosmic structures, distorting the apparent shapes of galaxies. This effect, known as weak lensing, is the most powerful cosmological probe of the next decade, and it can answer some of the biggest questions in cosmology: What are dark matter and dark energy, and how do cosmic structures form?

The standard approach to weak lensing analysis is to fit the two-point statistics of the data, such as the correlation function of the observed galaxy shapes. However, this data compression is sub- optimal and discards large amounts of information. This has led to the development of several approaches based on high-order statistics, such as third moments, wavelet phase harmonics and field-level analyses. These techniques provide more precise constraints on the parameters of the cosmological model (Ajani et al. 2023). However, with their increasing precision, these methods become sensitive to systematic effects that were negligible in the standard two-point statistics analyses.

One of these systematics is source clustering, which refers to the non-uniform distribution of the galaxies observed in weak lensing surveys. Rather than being uniformly distributed, the observed galaxies trace the underlying matter density. This clustering causes a correlation between the lensing signal and the galaxy number density, leading to two effects: (1) it modulates the effective redshift distribution of the galaxies, and (2) it correlates the galaxy shape noise with the lensing signal. Although this effect is negligible for two-point statistics (Krause et al. 2021, Linke et al. 2024), it significantly impacts the results of high-order statistics (Gatti et al. 2023). Therefore, accurate modelling of source clustering is critical to applying these new techniques to Euclid’s weak lensing data.

In this project, we will develop an inference framework to model source clustering and asses its impact on cosmological constraints from high-order statistics. The objectives of the project are:

1. Develop an inference framework that populates dark matter fields with galaxies, accurately modelling the non-uniform distribution of background galaxies in weak lensing surveys.

2. Quantify the source clustering impact on the cosmological parameters from wavelet transforms and field-level analyses.

3. Incorporate source clustering in emulators of the matter distribution to enable accurate data modelling in the high-order statistics analyses.

With these developments, this project will improve the accuracy of cosmological analyses and the realism of the data modelling, making high-order statistics analyses possible for Euclid data.