  We present a new inflation model, known as noncommutative decrumpling
inflation, in which space has noncommutative geometry with time variability of
the number of spatial dimensions. Within the framework of noncommutative
decrumpling inflation, we compute both the spectral index and its running. Our
results show that the effects of both time variability of the number of spatial
dimensions and noncommutative geometry on the spectral index and its running.
Two classes of examples have been studied and comparisons made with the
standard slow-roll formulae. We conclude that the effects of noncommutative
geometry on the spectral index and its running are much smaller than the
effects of time variability of spatial dimensions.
