Cosmological solution from D-brane motion in NS5-branes background

We study dynamics of a D3-brane propagating in the vicinity of k coincident NS5 branes. We show that when g(s) is small, there exists a regime in which dynamics of the D-brane is governed by Dirac-Born-Infeld action while higher order derivative in the expansion cannot be neglected. This leads to a restriction on how fast scalar field may roll. We analyze the motion of a rolling scalar field in this regime, and extend the analysis to cosmological systems obtained by coupling this type of field theory to four-dimensional gravity. It also leads to some FRW cosmologies, some of which are related to those obtained with tachyon matter.