The distribution of Omega_k from the scale-factor cutoff measure

TL;DR

This paper investigates how the scale-factor cutoff measure in eternal inflation models predicts the distribution of cosmic curvature, suggesting that observable curvature can constrain landscape inflation models.

Contribution

It introduces a model linking landscape inflation distributions with curvature predictions, providing a way to test multiverse theories against observations.

Findings

Approximately 10% chance of observable curvature above cosmic variance expectations.

Anthropic selection does not strongly favor minimal curvature, allowing observational bounds to constrain models.

Landscape models often predict insufficient inflation, which can be ruled out by current curvature measurements.

Abstract

Our universe may be contained in one among a diverging number of bubbles that nucleate within an eternally inflating multiverse. A promising measure to regulate the diverging spacetime volume of such a multiverse is the scale-factor cutoff, one feature of which is bubbles are not rewarded for having a longer duration of slow-roll inflation. Thus, depending on the landscape distribution of the number of e-folds of inflation among bubbles like ours, we might hope to measure spacetime curvature. We study a recently proposed cartoon model of inflation in the landscape and find a reasonable chance (about ten percent) that the curvature in our universe is well above the value expected from cosmic variance. Anthropic selection does not strongly select for curvature as small as is observed (relative somewhat larger values), meaning the observational bound on curvature can be used to rule out landscape models that typically give too little inflation.