  Recent Planck measurements show some CMB anomalies on large angular scales,
which confirms the early observations by WMAP. We show that an inflationary
model, in which before the slow-roll inflation the Universe is in a
superinflationary phase, can generate a large-scale cutoff in the primordial
power spectrum, which may account for not only the power suppression on large
angular scales, but also a large dipole power asymmetry in the CMB. We discuss
an implementation of our model in string theory.
