  We study D-brane dynamics in the gravity dual background of ODp theories
using the effective action on the worldvolume of the brane. We explore the
similarities of the system with the rolling tachyon, including the exponential
decrease of pressure at late times. We also consider the case where the
worldvolume theory on a D3-brane is coupled to gravity and construct a
cosmological model. By considering the time reversal symmetric solutions, we
find that we can have both closed and open universes depending on the initial
value of the radial mode on the brane. We compare the models with tachyon
driven cosmologies and find limits where slow roll inflation is realized.
