2010/05/31 by Raphael Bousso, Ben Freivogel, Stefan Leichenauer +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Causal structure #Classical mechanics #Conformal map #Cosmology and Gravitation Theories #Cutoff #Einstein #Eternal inflation #Galaxies: Formation, Evolution, Phenomena #Geodesic #Inflation (cosmology) #Mathematical analysis #Mathematics #Measure (data warehouse) #Physics #Quantum mechanics #Theoretical physics #astro-ph.CO #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.82.125032
published as Phys.Rev.D82:125032,2010 · 39 pages, 4 figures; v2: minor corrections
arxiv created 2010/09/18 · openalex publication_date 2010/12/22 · arxiv updated 2015/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose to regulate the infinities of eternal inflation by relating a late time cutoff in the bulk to a short-distance cutoff 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 Friedmann-Robertson-Walker approximation for bubble universes. Remarkably, we find that the future boundary becomes a round three-sphere, with smooth metric on all scales. Our cutoff 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.