  In the slow-roll inflationary scenario, the amplitude of the curvature
perturbations approaches a constant value soon after the modes leave the Hubble
radius. However, relatively recently, it was shown that the amplitude of the
curvature perturbations induced by the canonical scalar field can grow at
super-Hubble scales if there is either a transition to fast roll inflation or
if inflation is interrupted for some period of time. In this work, we extend
the earlier analysis to the case of a non-canonical scalar field described by
the Dirac-Born-Infeld action. With the help of a specific example, we show that
the amplitude of the tachyonic perturbations can be enhanced or suppressed at
super-Hubble scales if there is a transition from slow roll to fast roll
inflation. We also illustrate as to how the growth of the entropy perturbations
during the fast roll regime proves to be responsible for the change in the
amplitude of the curvature perturbations at super-Hubble scales. Furthermore,
following the earlier analysis for the canonical scalar field, we show that the
power spectrum evaluated in the long wavelength approximation matches the exact
power spectrum obtained numerically very well. Finally, we briefly comment on
an application of this phenomenon.
