  We study the bounds on tensor wave in a class of twisted inflation models
where $D(4+2k)$-branes are wrapped on cycles in the compact manifold and wrap
the KK-direction in the corresponding effective field theory. While the lower
bound is found to be analogous to that in Type IIB models of brane inflation,
the upper bound turns out to be significantly different. This is argued for a
range of values for the parameter $g_s M$ satisfying the self-consistency
relation and the WMAP data. Further, we observe that the wrapped $D8$-brane
appears to be the most attractive from a cosmological perspective.
