  We study the braneworld theory constructed by multi scalar fields. The model
contains a smooth and infinitely large extra dimension, allowing the background
fields propagating in it. We give a de Sitter solution for the four-dimensional
cosmology as a good approximation to the early universe inflation. We show that
the graviton has a localizable massless mode, and a series of continuous
massive modes, separated by a mass gap. There could be a normalizable massive
mode, depending on the background solution. The gravitational waves of massless
mode evolve the same as the four dimensional theory, while that of the massive
modes evolve greatly different from the massless mode.
