Replication regulates volume weighting in quantum cosmology

James Hartle and Thomas Hertog
Phys. Rev. D 80, 063531 – Published 25 September 2009

Abstract

Probabilities for observations in cosmology are conditioned both on the Universe’s quantum state and on local data specifying the observational situation. We show the quantum state defines a measure for prediction through such conditional probabilities that is well-behaved for spatially large or infinite universes when the probabilities that our data are replicated are taken into account. In histories where our data are rare volume weighting connects top-down probabilities conditioned on both the data and the quantum state to the bottom-up probabilities conditioned on the quantum state alone. We apply these principles to a calculation of the number of inflationary e-folds in a homogeneous, isotropic minisuperspace model with a single scalar field moving in a quadratic potential. We find that volume weighting is justified and the top-down probabilities favor a large number of e-folds, hereby predicting the curvature of our Universe at the present time to be approximately zero.

  • Figure
  • Figure
  • Received 1 August 2009

DOI:https://doi.org/10.1103/PhysRevD.80.063531

©2009 American Physical Society

Authors & Affiliations

James Hartle1 and Thomas Hertog2

  • 1Department of Physics, University of California, Santa Barbara, California 93106, USA
  • 2APC, UMR 7164 (CNRS, Université Paris 7), 10 rue A.Domon et L.Duquet, 75205 Paris, France and Intl Solvay Institutes, Boulevard du Triomphe, ULB-C.P. 231, 1050 Brussels, Belgium

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 80, Iss. 6 — 15 September 2009

Reuse & Permissions
Access Options

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×