  We investigate an inflationary model of the universe based on the assumption
that space-time is noncommutative in the very early universe. We analyze the
effects of space-time noncommutativity on the quantum fluctuations of an
inflaton field and investigate their contributions to the cosmic microwave
background (CMB). We show that the angular power spectrum l(l+1)C_l generically
has a sharp damping for lower l if we assume that the last scattering surface
is traced back to fuzzy spheres at the times when large-scale modes cross the
Hubble horizon.
