Measure problem in cosmology
Abstract
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 FriedmannLemaitreRobertsonWalker 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 efolds of inflation in singlefield, slowroll models is suppressed by of order exp(3N) and we discuss the implications of this result.
 Publication:

Physical Review D
 Pub Date:
 March 2008
 DOI:
 10.1103/PhysRevD.77.063516
 arXiv:
 arXiv:hepth/0609095
 Bibcode:
 2008PhRvD..77f3516G
 Keywords:

 98.80.Cq;
 04.60.Kz;
 12.10.Dm;
 Particletheory and fieldtheory models of the early Universe;
 Lower dimensional models;
 minisuperspace models;
 Unified theories and models of strong and electroweak interactions;
 High Energy Physics  Theory;
 Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 22 pages, 6 figures. Revised version with clarifying remarks on meaning of adopted measure, extra references and minor typographical corrections