We study a class of N = 1 Supergravity inflationary models in which the evolution of the inflaton dynamics is controlled by a single power in the inflaton field at the point where the observed density fluctuations are produced , in the context of the braneworld scenario , in light of WMAP results .
In particular , we find that the bounds on the spectral index and its running constrain the parameter space both for models where the inflationary potential is dominated by a quadratic term and by a cubic term in the inflaton field .
We also find that \alpha _ { s } > 0 is required for the quadratic model whereas \alpha _ { s } < 0 
for the cubic model .
Moreover , we have determined an upper bound on the five-dimensional Planck scale , M _ { 5 } \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ < $ } } % 0.019 M , for the quadratic model .
On the other hand , a running spectral index with n _ { s } > 1 on large scales and n _ { s } < 1 on small scales is not possible in either case .