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Physical Review Letters 100 (2008) 202301
The No-Boundary Measure of the Universe
J.B. Hartle1, S.W. Hawking2, T. Hertog3, 4

We consider the no-boundary proposal for homogeneous isotropic closed universes with a cosmological constant and a scalar field with a quadratic potential. In the semi-classical limit, it predicts classical behavior at late times if the initial scalar field is more than a certain minimum. If the classical late time histories are extended back, they may be singular or bounce at a finite radius. The no-boundary proposal provides a probability measure on the classical solutions which selects inflationary histories but is heavily biased towards small amounts of inflation. This would not be compatible with observations. However we argue that the probability for a homogeneous universe should be multiplied by exp(3N) where N is the number of e-foldings of slow roll inflation to obtain the probability for what we observe in our past light cone. This volume weighting is similar to that in eternal inflation but derived in a gauge invariant manner and without redundant bubble universes outside our past light cone. In a landscape potential, it would predict that the universe would have a large amount of inflation and that it would start in an approximately de Sitter state near a saddle-point of the potential. The universe would then have always been in the semi-classical regime.
1 :  Departement of Physics, University of California
2 :  DAMTP/CMS - Department of Applied Mathematics and Theoretical Physics / Centre for Mathematical Sciences
3 :  APC - UMR 7164 - AstroParticule et Cosmologie
4 :  International Solvay Institutes
Physique/Physique des Hautes Energies - Théorie

Physique/Astrophysique/Cosmologie et astrophysique extra-galactique

Planète et Univers/Astrophysique/Cosmologie et astrophysique extra-galactique

Physique/Relativité Générale et Cosmologie Quantique

Planète et Univers/Astrophysique
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