Boundary definition of a multiverse measure - High Energy Physics - TheoryReport as inadecuate

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Abstract: We propose to regulate the infinities of eternal inflation by relating a latetime 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 futurelight-cone on the boundary. We seek an intrinsic definition of boundary volumesthat makes no reference to bulk structures. This requires taming the fractalgeometry of the future boundary, and lifting the ambiguity of the conformalfactor. We propose to work in the conformal frame in which the boundary Ricciscalar is constant. We explore this proposal in the FRW approximation forbubble universes. Remarkably, we find that the future boundary becomes a roundthree-sphere, with smooth metric on all scales. Our cut-off yields the samerelative probabilities as a previous proposal that defined boundary volumes byprojection into the bulk along timelike geodesics. Moreover, it is equivalentto an ensemble of causal patches defined without reference to bulk geodesics.It thus yields a holographically motivated and phenomenologically successfulmeasure for eternal inflation.

Author: Raphael Bousso, Ben Freivogel, Stefan Leichenauer, Vladimir Rosenhaus


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