  We study the preheating process in a model of DBI inflation with a DBI-type
inflaton coupling to a canonical entropy field. At the end of inflation, the
inflaton field oscillates around its vacuum which can arise from an infrared
cutoff parameter on the warp factor and correspondingly the evolution of its
fluctuations can be approximately described by a generalized Hill's equation in
third order. We study the field fluctuations numerically and show that they
could grow exponentially since the instability bands commonly exist in the DBI
models if the amplitudes of background oscillations are of order or larger than
the cutoff parameter. Our numerical result also reveals that the particle
excitation of the matter field is more dramatic than that in usual case since
the parametric resonance lasts longer when the effect of a warp factor is taken
into account. Therefore, we conclude that the preheating process in the model
of DBI inflation could be more efficient than that in standard inflation
models.
