Boundary definition of a multiverse measure
  We propose to regulate the infinities of eternal inflation by relating a late
time cut-off in the bulk to a short distance cut-off on the future boundary.
The light-cone time of an event is defined in terms of the volume of its future
light-cone on the boundary. We seek an intrinsic definition of boundary volumes
that makes no reference to bulk structures. This requires taming the fractal
geometry of the future boundary, and lifting the ambiguity of the conformal
factor. We propose to work in the conformal frame in which the boundary Ricci
scalar is constant. We explore this proposal in the FRW approximation for
bubble universes. Remarkably, we find that the future boundary becomes a round
three-sphere, with smooth metric on all scales. Our cut-off yields the same
relative probabilities as a previous proposal that defined boundary volumes by
projection into the bulk along timelike geodesics. Moreover, it is equivalent
to an ensemble of causal patches defined without reference to bulk geodesics.
It thus yields a holographically motivated and phenomenologically successful
measure for eternal inflation.
