CLASSICAL ANISOTROPIES IN MODELS OF OPEN INFLATION

In the simplest model of open inflation there are two inflaton fields decoupled from each other. One of them, the tunneling field, produces a first stage of inflation which prepares the ground for the nucleatio n of a highly symmetric bubble. The other, a free field, drives a seco nd period of slow-roll inflation inside the bubble. However, the secon d field also evolves during the first stage of inflation, which to som e extent breaks the needed symmetry. We show that this generates large supercurvature anisotropies which, together with the results of Tanak a and Sasaki, rule out this class of simple models (unless, of course, no is sufficiently close to 1). The problem does not arise in modifie d models where the second field does not evolve in the first stage of inflation.