Confronting brane inflation with Planck and pre-Planck data

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In this paper, we compare brane inflation models with the Planck data and the pre-Planck data (which combines WAMP, ACT, SPT, BAO and ${H}_{0}$ data). The Planck data prefer a spectral index less than unity at more than $5\ensuremath{\sigma}$ confidence level, and a running of the spectral index at around $2\ensuremath{\sigma}$ confidence level. We find that the KKLMMT model can survive at the level of $2\ensuremath{\sigma}$ only if the parameter $\ensuremath{\beta}$ (the conformal coupling between the Hubble parameter and the inflaton) is less than $\mathcal{O}({10}^{\ensuremath{-}3})$, which indicates a certain level of fine-tuning. The IR DBI model can provide a slightly larger negative running of spectral index and red tilt, but in order to be consistent with the non-Gaussianity constraints from Planck, its parameter also needs fine-tuning at some level.