Treatment of caustics in Vlasov perturbation theory

Determine how caustic formation is treated within Vlasov perturbation theory applied to cosmological large-scale structure, providing a clear and consistent formulation for handling caustics in this primarily Newtonian framework.

Background

The authors survey current approaches beyond linear scales and note that Vlasov perturbation theory, though promising, is primarily Newtonian and lacks a clear treatment of caustics. This gap becomes critical when addressing shell-crossing and multi-stream regimes in structure formation.

Their proposed approach incorporates backreaction via boundary terms at matter horizons, but they explicitly identify the unresolved status of caustic treatment within Vlasov perturbation theory.