Replication Regulates Volume Weighting in Quantum Cosmology

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 is 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.

13 pages, 3 figures; v2: correction case of data on multiple surfaces, clarification objectivity

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• Predicting a Prior for Planck
• Anthropic Bounds on Lambda from the No-Boundary Quantum State
• CFT driven cosmology and conformal higher spin fields
• New type of hill-top inflation
• Topological Inflation
• Sharp Predictions from Eternal Inflation Patches in D-brane Inflation
• Possible Anthropic Support for a Decaying Universe: A Cosmic Doomsday Argument
• Path Integral for Stochastic Inflation: Non-Perturbative Volume Weighting, Complex Histories, Initial Conditions and the End of Inflation
• Spacetime Average Density (SAD) Cosmological Measures
• Delicate curvature bounces in the no-boundary wave function and in the late universe
• Comment on Coleman-DeLuccia Instantons