Inferring galaxy cluster masses from cosmic microwave background lensing with neural simulation based inference

Gravitational lensing by massive galaxy clusters distorts the observed cosmic microwave background (CMB) on arcminute scales, and these distortions carry information about cluster masses. Standard approaches to extracting cluster mass constraints from the CMB cluster lensing signal are either sub-optimal, ignore important physical or observational effects, are computationally intractable, or require additional work to turn the lensing measurements into constraints on cluster masses. We apply simulation based inference (SBI) using neural likelihood models to the problem. We show that in circumstances where the exact likelihood can be computed, the SBI constraints on cluster masses are in agreement with the exact likelihood, demonstrating that the SBI constraints are close to optimal. In scenarios where the exact likelihood cannot be feasibly computed, SBI still recovers unbiased estimates of individual cluster masses and combined constraints from multiple clusters. SBI will be a powerful tool for constraining the masses of galaxy clusters detected by future cosmic surveys. Code to run the analyses presented here will be made publicly available.