Uncertainties of predictions in models of eternal inflation

TL;DR

This paper examines how uncertainties in modeling eternal inflation arise from choices of time variables and factor ordering, demonstrating that these uncertainties are comparable and the results are robust within these variations.

Contribution

It analyzes the dependence of eternal inflation predictions on time parametrization and factor ordering, showing the results are stable within their inherent ambiguities.

Findings

Variation due to factor ordering is comparable to that from time variable choice.

Results are effectively independent of the specific time parametrization within accuracy.

Analytical and numerical methods confirm the robustness of the predictions.

Abstract

In a previous paper \cite{MakingPredictions}, a method of comparing the volumes of thermalized regions in eternally inflating universe was introduced. In this paper, we investigate the dependence of the results obtained through that method on the choice of the time variable and factor ordering in the diffusion equation that describes the evolution of eternally inflating universes. It is shown, both analytically and numerically, that the variation of the results due to factor ordering ambiguity inherent in the model is of the same order as their variation due to the choice of the time variable. Therefore, the results are, within their accuracy, free of the spurious dependence on the time parametrization.