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We compute the probability distribution for bubble collisions in an inflatingfalse vacuum which decays by bubble nucleation. Our analysis generalizesprevious work of Guth, Garriga, and Vilenkin to the case of generalcosmological evolution inside the bubble, and takes into account the dynamicsof the domain walls that form between the colliding bubbles. We find thatincorporating these effects changes the results dramatically: the totalexpected number of bubble collisions in the past lightcone of a typicalobserver is N ~ \gamma V_f / V_i, where \gamma is the fastest decay rate of thefalse vacuum, V_f is its vacuum energy, and V_i is the vacuum energy duringinflation inside the bubble. This number can be large in realistic modelswithout tuning. In addition, we calculate the angular position and sizedistribution of the collisions on the cosmic microwave background sky, anddemonstrate that the number of bubbles of observable angular size is N_{LS}\sim \sqrt{\Omega_k} N, where \Omega_k is the curvature contribution to thetotal density at the time of observation. The distribution is almost exactlyisotropic.

Eternal Inflation, Bubble Collisions, and the Disintegration of the Persistence of Memory