Is brane inflation eternal?

Abstract

In this paper, we show that eternal inflation of the random walk type is generically absent in thebrane inflationary scenario. Depending on how the brane inflationary universe originated, eternalinflation of the false vacuum type is still quite possible. Since inflaton is the position of theD3-brane relative to the D̄3-brane inside the compactified bulk with finite size, its value is bounded. In DBI inflation,the warped space also restricts the amplitude of the scalar fluctuation. These upper boundsimpose strong constraints on the possibility of eternal inflation. We find that eternalinflation due to the random walk of the inflaton field is absent in both the KKLMMTslow-roll scenario and the DBI scenario. A more careful analysis for the slow-roll case isalso presented using the Langevin equation, which gives very similar results. We discusspossible ways to obtain eternal inflation of the random walk type in brane inflation. In themulti-throat brane inflationary scenario, the branes may be generated by quantumtunnelling and roll out the throat. Eternal inflation of the false vacuum type inevitablyhappens in this scenario due to the tunnelling process. Since these scenarios havedifferent cosmological predictions, more data from the cosmic microwave backgroundradiation will hopefully select the specific scenario our universe has gone through.