2006/09/30 by G. W. Gibbons, Neil Turok · 200 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Computer science #Cosmology #Cosmology and Gravitation Theories #Divergence (linguistics) #Einstein #Galaxies: Formation, Evolution, Phenomena #General relativity #Inflation (cosmology) #Mathematical analysis #Mathematics #Measure (data warehouse) #Phase space #Physics #Probability measure #Quantum mechanics #Scalar field #Theoretical physics #Universe #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.77.063516
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 77(6) (American Physical Society) · 22 pages, 6 figures. Revised version with clarifying remarks on meaning of adopted measure, extra references and minor typographical corrections
arxiv created 2007/01/02 · openalex publication_date 2008/03/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Hamiltonian structure of general relativity provides a natural canonical measure on the space of all classical universes, i.e., the multiverse. We review this construction and show how one can visualize the measure in terms of a ``magnetic flux'' of solutions through phase space. Previous studies identified a divergence in the measure, which we observe to be due to the dilatation invariance of flat Friedmann-Lemaitre-Robertson-Walker universes. We show that the divergence is removed if we identify universes which are so flat they cannot be observationally distinguished. The resulting measure is independent of time and of the choice of coordinates on the space of fields. We further show that, for some quantities of interest, the measure is very insensitive to the details of how the identification is made. One such quantity is the probability of inflation in simple scalar field models. We find that, according to our implementation of the canonical measure, the probability for N e-folds of inflation in single-field, slow-roll models is suppressed by of order exp(\ensuremath-3N) and we discuss the implications of this result.