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.

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