If our Universe is a 3+1 brane in a warped 4+1 dimensional bulk so that its expansion can be understood as the motion of the brane in the bulk, the time dependence of the boundary conditions for arbitrary bulk fields can lead to particle creation via the dynamical Casimir effect. In this talk I report results for the simplest such scenario, when the only particle in the bulk is the graviton and the bulk is the 5 dimensional anti-de Sitter spacetime.