Replication Regulates Volume Weighting in Quantum Cosmology

TL;DR

This paper demonstrates how volume weighting in quantum cosmology, when accounting for data replication, influences predictions of inflationary e-folds, favoring large inflation scenarios.

Contribution

It introduces a measure for prediction in quantum cosmology that remains well-behaved in large universes by incorporating data replication effects.

Findings

Volume weighting connects top-down and bottom-up probabilities.

Top-down probabilities favor a large number of inflationary e-folds.

The measure justifies volume weighting in cosmological predictions.

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.