The distribution of Omega_k from the scale-factor cutoff measure
  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.
