DBI Inflation and Warped Black Holes
  We study a possible amplification mechanism for the curvature perturbations
generated during inflation by a Dirac-Born-Infeld (DBI) inflaton in the
presence of a sharp feature in the warp factor. The large growth resulting in
the scalar power spectrum is a consequence of the decreasing speed of sound. We
obtain analytical approximate expressions for the relevant dynamical quantities
both in the slow roll phase and during the transient phase which leads to the
amplification. We finally compare our approximations to the exact numerical
evolution and give, in such a context, the general rules for building a viable
inflationary model leading to, during the subsequent radiation dominated era,
an abundant primordial black holes formation.
