Brane inflation and the overshoot problem

We investigate recent claims that brane inflation solves the overshoot problem through a combination of microphysical restrictions on the phase space of initial conditions and the existence of the Dirac-Born-Infeld attractor in regimes where the slow-roll attractor does not apply. Carrying out a comprehensive analysis of the parameter space allowed by the latest advances in brane inflation model-building, we find that these restrictions are insufficient to solve the overshoot problem. The vast majority of the phase space of initial conditions is still dominated by overshoot trajectories. We present an analytic proof that the brane-inflationary attractor must be close to the slow-roll limit, and update the predictions for observables such as non-Gaussianity, cosmic string tension, and tensor modes.