  We discuss D-braneworld cosmology, that is, the brane is described by the
Born-Infeld action. Compared with the usual Randall-Sundrum braneworld
cosmology where the brane action is the Nambu-Goto one, we can see some drastic
changes at the very early universe: (i)universe may experience the rapid
accelerating phase (ii)the closed universe may avoid the initial singularity.
We also briefly address the dynamics of the cosmology in the open string
metric, which might be favorer than the induced metric from the view point of
the D-brane.
