  We study the generation and evolution of gravitational waves (tensor
perturbations) in the context of Randall-Sundrum braneworld cosmology. We
assume that the initial and final stages of the background cosmological model
are given by de Sitter and Minkowski phases, respectively, and they are
connected smoothly by a radiation-dominated phase. This setup allows us to
discuss the quantum-mechanical generation of the perturbations and to see the
final amplitude of the well-defined zero mode. Using the Wronskian formulation,
we numerically compute the power spectrum of gravitational waves, and find that
the effect of initial vacuum fluctuations in the Kaluza-Klein modes is
subdominant, contributing not more than 10% of the total power spectrum. Thus
it is confirmed that the damping due to the Kaluza-Klein mode generation and
the enhancement due to the modification of the background Friedmann equation
are the two dominant effects, but they cancel each other, leading to the same
spectral tilt as the standard four-dimensional result. Kaluza-Klein gravitons
that escape from the brane contribute to the energy density of the dark
radiation at late times. We show that a tiny amount of the dark radiation is
generated due to this process.
