Observing the Geometry of Warped Compactification via Cosmic Inflation

Using Dirac-Born-Infeld inflation as an example, we demonstrate that the detailed geometry of warped compactification can leave an imprint on the cosmic microwave background. We compute cosmic microwave background observables for Dirac-Born-Infeld inflation in a generic class of warped throats and find that the results (such as the sign of the tilt of the scalar perturbations and its running) depend sensitively on the precise shape of the warp factor. In particular, we analyze the warped deformed conifold and find that the results can differ from those of other warped geometries, even when these geometries approximate well the exact metric of the warped deformed conifold.