BUBBLE FLUCTUATIONS IN OMEGA-LESS-THAN-1 INFLATION

in the context of the open inflationary universe, we calculate the amp litude of quantum fluctuations which deform the bubble shape. These gi ve rise ro scalar field fluctuations in the open Friedmann-Robertson-W alker universe which is contained inside the bubble. One can transform to a new gauge in which matter looks perfectly smooth, and then the p erturbations behave as tensor modes (gravitational waves of very long wavelength). For (1 - Omega) much less than 1, where Omega is the dens ity parameter, the microwave temperature anisotropies produced by thes e modes are of order delta T/T similar to H(R(0) mu l)(-1/2)(1 - Omega )(1/2). Here, H is the expansion rate during inflation, ii, is the int rinsic radius of the bubble at the time of nucleation, mu is the bubbl e wall tension, and I labels the different multipoles (l > 1). The gra vitational back reaction of the bubble has been ignored, In this appro ximation, G mu R(0) much less than 1, and the new effect can be much l arger than the one due to ordinary gravitational waves generated durin g inflation (unless, of course Omega gets too close to 1, in which cas e the new effect disappears).