On wave propagation in the Anti-de Sitter cosmology

Abstract

We investigate the Klein–Gordon equation on the Poincaré patch of the 5-dimensional Anti-de Sitter universe. Despite the loss of the global hyperbolicity, the Cauchy problem is well-posed in the space of the finite energy data. We establish several results of asymptotic behaviours. We consider also the cosmological model of the Minkowski brane with a negative tension, for which we solve the mixed problem.