Abstract：

Galaxy clusters, the largest gravitationally bound structures in the Universe, are key to understanding the interplay between cosmology and astrophysical processes. Multi-probe analyses, combining gravitational lensing, X-ray, and spectroscopic observations, provide critical insights into the properties of dark matter, its interactions with baryons, and its role in driving nonlinear structure formation. In this talk, I will present new approaches to these fundamental questions. First, I will discuss how the radial acceleration relation in galaxy clusters can constrain the self-interaction cross-section of dark matter (Tam, Umetsu, Robertson, & McCarthy 2023). Next, I will introduce a method that combines gravitational lensing and phase-space observations to measure the matter distribution from cluster cores to their outskirts and into the surrounding cosmic web. These outer regions, where mass accretion and cosmic acceleration shape cluster growth, offer a unique perspective on nonlinear structure formation and fundamental cosmology. This work is especially timely in today’s era of large-scale imaging and redshift surveys.