Phenomenology of D-brane inflation with general speed of sound

A characteristic of D-brane inflation is that fluctuations in the inflaton field can propagate at a speed significantly less than the speed of light. This yields observable effects that are distinct from those of single-field slow-roll inflation, such as a modification of the inflationary consistency relation and a potentially large level of non-Gaussianities. We present a numerical algorithm that extends the inflationary flow formalism to models with general speed of sound. For an ensemble of D-brane-inflation models parametrized by the Hubble parameter and the speed of sound as polynomial functions of the inflaton field, we give qualitative predictions for the key inflationary observables. We discuss various consistency relations for D-brane inflation, and compare the qualitative shapes of the warp factors we derive from the numerical models with analytical warp factors considered in the literature. Finally, we derive and apply a generalized microphysical bound on the inflaton field variation during brane inflation. While a large number of models are consistent with current cosmological constraints, almost all of these models violate the compactification constraint on the field range in four-dimensional Planck units. If the field range bound is to hold, then models with a detectable level of non-Gaussianity predict a blue scalar spectral index, and a tensor component that is far below the detection limit of any future experiment.