The CMB and the measure of the multiverse
  In the context of eternal inflation, cosmological predictions depend on the
choice of measure to regulate the diverging spacetime volume. The spectrum of
inflationary perturbations is no exception, as we demonstrate by comparing the
predictions of the fat geodesic and causal patch measures. To highlight the
effect of the measure---as opposed to any effects related to a possible
landscape of vacua---we take the cosmological model, including the model of
inflation, to be fixed. We also condition on the average CMB temperature
accompanying the measurement. Both measures predict a 1-point expectation value
for the gauge-invariant Newtonian potential, which takes the form of a
(scale-dependent) monopole, in addition to a related contribution to the
3-point correlation function, with the detailed form of these quantities
differing between the measures. However, for both measures both effects are
well within cosmic variance. Our results make clear the theoretical relevance
of the measure, and at the same time validate the standard inflationary
predictions in the context of eternal inflation.
