Eternal observers and bubble abundances in the landscape
  We study a class of ``landscape'' models in which all vacua have positive energy density, so that inflation never ends and bubbles of different vacua are endlessly ``recycled''. In such models, each geodesic observer passes through an infinite sequence of bubbles, visiting all possible kinds of vacua. The bubble abundance $p_j$ can then be defined as the frequency at which bubbles of type $j$ are visited along the worldline of an observer. We compare this definition with the recently proposed general prescription for $p_j$ and show that they give identical results. 
Vitaly Vanchurin and Alexander Vilenkin