Can topological analyses of weak-lensing convergence maps constrain neutrino mass?

Determine whether topological analyses applied directly to weak lensing convergence maps can constrain the sum of neutrino masses from cosmological data, despite the information loss caused by projecting three-dimensional structure onto two-dimensional convergence fields.

Background

The paper demonstrates that topological statistics based on persistent homology can be highly sensitive to the sum of neutrino masses when applied to three-dimensional total matter fields. Since weak lensing directly probes the total matter distribution, extending these topological methods to weak lensing data is a natural direction for observational applications.

However, weak lensing convergence maps are line-of-sight projections that compress three-dimensional structure into two dimensions, leading to information loss that may limit the constraining power of topological statistics. Although tomographic binning can partially mitigate this issue and recent work has shown the feasibility of applying persistent homology to weak lensing, it remains unresolved whether such an approach can robustly constrain neutrino masses.