  We study the quantum-mechanical generation of gravitational waves during
inflation on a brane embedded in a five-dimensional anti-de Sitter bulk. To
make the problem well-posed, we consider the setup in which both initial and
final phases are given by a de Sitter brane with different values of the Hubble
expansion rate. Assuming that the quantum state is in a de Sitter invariant
vacuum in the initial de Sitter phase, we numerically evaluate the amplitude of
quantum fluctuations of the growing solution of the zero mode in the final de
Sitter phase. We find that the vacuum fluctuations of the initial Kaluza-Klein
gravitons as well as of the zero mode gravitons contribute to the final
amplitude of the zero mode on small scales, and the power spectrum is quite
well approximated by what we call the rescaled spectrum, which is obtained by
rescaling the standard four-dimensional calculation following a simple mapping
rule. Our results confirm the speculation raised in Ref.
\cite{Kobayashi:2003cn} before.
