Abstract
In this paper we investigate the Klein–Gordon equation in the past causal domain of a de Sitter brane imbedded in an Anti-de Sitter bulk. We solve the global mixed hyperbolic problem. We prove that any finite energy solution can be expressed as a Kaluza–Klein tower that is a superposition of free fields in the Steady State Universe, of which we study the asymptotic behaviours. We show that the leading term of a gravitational fluctuation is a massless graviton, i.e. the de Sitter brane is linearly stable. Beyond the Cauchy horizon, the energy of the waves can tend to infinity at the moment the brane hits the conformal time-like boundary.
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