No-Boundary Measure of the Universe

James B. Hartle, S. W. Hawking, and Thomas Hertog
Phys. Rev. Lett. 100, 201301 – Published 23 May 2008
An article within the collection: The Work of Stephen Hawking in Physical Review

Abstract

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 semiclassical limit, it predicts classical behavior at late times if the scalar field is large enough. The classical histories may be singular in the past or bounce at a finite radius. This probability measure selects inflationary histories but is biased towards small numbers of e-foldings N. However, to obtain the probability of our observations in our past light cone these probabilities should be multiplied by exp(3N). This volume weighting is similar to that in eternal inflation. In a landscape potential, it would predict that the Universe underwent a large amount of inflation and could have always been semiclassical.

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  • Received 8 February 2008

DOI:https://doi.org/10.1103/PhysRevLett.100.201301

©2008 American Physical Society

Collections

This article appears in the following collection:

The Work of Stephen Hawking in Physical Review

To mark the passing of Stephen Hawking, we gathered together his 55 papers in Physical Review D and Physical Review Letters. They probe the edges of space and time, from "Black holes and thermodynamics” to "Wave function of the Universe."

Authors & Affiliations

James B. Hartle1, S. W. Hawking2, and Thomas Hertog3

  • 1Department of Physics, University of California, Santa Barbara, 93106, USA
  • 2DAMTP, CMS, Wilberforce Road, CB3 0WA Cambridge, United Kingdom
  • 3Laboratoire APC, Université Paris 7, 10 rue A.Domon et L.Duquet, 75205 Paris, France and International Solvay Institutes, Boulevard du Triomphe, ULB-C.P. 231, 1050 Brussels, Belgium

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Issue

Vol. 100, Iss. 20 — 23 May 2008

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