Graviton production in brane worlds by the dynamical Casimir effect

Abstract

Abstract. 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.

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

“…As we have shown in [12], the BC's (15) and (16) are indeed the only ones for which S h ¼ 0 leads to the free wave Eq. (14). (In principle also Dirichlet BC's, i.e.…”

“…The perturbed Einstein equations and the second junction condition lead to the boundary value problem @ 2 t þ k 2 À @ 2 y þ 3 y @ y hðt; y; kÞ ¼ 0 in the bulk (14) and ðv@ t þ @ y Þhj y b ðtÞ ¼ 0…”

“…However, in order to solve the problem, we have neglected the velocity term in the BC (15). The ansatz…”

“…This problem prompted us to search for another description allowing us to treat the boundary condition (15) in full.…”

“…In Poincaré coordinates the nontriviality of the time-evolution of the perturbations is purely a con- sequence of the time-dependent junction condition, no time-dependent functions enter the wave Eq. (14). Our coordinate transformation which transforms the generalized Neumann BC into a pure Neumann BC, induces explicite time-dependence in the wave equation itself.…”