Fine-tuning in DBI inflationary mechanism

We show a model-independent fine-tuning issue in the DBI inflationary mechanism. DBI inflation requires a warp factor h small enough to sufficiently slow down the inflation. On the other hand, the Einstein equation in extra dimensions under the inflationary background deforms the warp space on the IR side. Generically these two locations coincide with each other, spoiling the DBI inflation. The origin and tuning of this 'h problem' is closely related, through the AdS/CFT duality, to those of the well-known 'eta problem' in the slow-roll inflationary mechanism.