Warp features in DBI inflation

In Dirac-Born-Infeld inflation, changes in the sound speed that transiently break the slow roll approximation lead to features in the power spectrum. We develop and test the generalized slow roll approximation for calculating such effects and show that it can be extended to treat order unity features. As in slow-roll, model independent constraints on the potential of canonical inflation can be directly reinterpreted in the DBI context through this approximation. In particular, a sharp horizon scale step in the warped brane tension can explain oscillatory features in the WMAP7 CMB power spectrum as well as features in the potential. Differences appear only as a small suppression of power on horizon scales and larger.