  We reconsider a string theoretic inflationary model, where inflation is
driven by $n$ multiple coincident $D3$-branes in the finite $n$ limit. We show
that the finite $n$ action can be continued to the limit of large $n$, where it
converges to the action for a wrapped $D5$-brane with $n$ units of U(1) flux.
This provides an important consistency check of the scenario and allows for
more control over certain back-reaction effects. We determine the most general
form of the action for a specific sub-class of models and examine the
non-relativistic limits of the theory where the branes move at speeds much less
than the speed of light. The non-Abelian nature of the world-volume theory
implies that the inflaton field is matrix valued and this results in
modifications to the slow-roll parameters and Hubble-flow equations. A specific
small field model of inflation is investigated where the branes move out of an
AdS throat, and observational constraints are employed to place bounds on the
background fluxes.
