Graviton production in anti-de Sitter braneworld cosmology: A fully consistent treatment of the boundary condition

In recent work by two of us, [Durrer and Ruser, Phys. Rev. Lett. 99, 071601 (2007); Ruser and Durrer Phys. Rev. D 76, 104014 (2007)], graviton production due to a moving spacetime boundary (braneworld) in a five dimensional bulk has been considered. In the same way as the presence of a conducting plate modifies the electromagnetic vacuum, the presence of a brane modifies the graviton vacuum. As the brane moves, the time dependence of the resulting boundary condition leads to particle creation via the so-called 'dynamical Casimir effect'. In our previous work a term in the boundary condition which is linear in the brane velocity has been neglected. In this work we develop a new approach which overcomes this approximation. We show that the previous results are not modified if the brane velocity is low.