Forecasting constraints from the cosmic microwave background on eternal
  inflation
  We forecast the ability of cosmic microwave background (CMB) temperature and
polarization datasets to constrain theories of eternal inflation using cosmic
bubble collisions. Using the Fisher matrix formalism, we determine both the
overall detectability of bubble collisions and the constraints achievable on
the fundamental parameters describing the underlying theory. The CMB signatures
considered are based on state-of-the-art numerical relativistic simulations of
the bubble collision spacetime, evolved using the full temperature and
polarization transfer functions. Comparing a theoretical
cosmic-variance-limited experiment to the WMAP and Planck satellites, we find
that there is no improvement to be gained from future temperature data, that
adding polarization improves detectability by approximately 30%, and that
cosmic-variance-limited polarization data offer only marginal improvements over
Planck. The fundamental parameter constraints achievable depend on the precise
values of the tensor-to-scalar ratio and energy density in (negative) spatial
curvature. For a tensor-to-scalar ratio of $0.1$ and spatial curvature at the
level of $10^{-4}$, using cosmic-variance-limited data it is possible to
measure the width of the potential barrier separating the inflating false
vacuum from the true vacuum down to $M_{\rm Pl}/500$, and the initial proper
distance between colliding bubbles to a factor $\pi/2$ of the false vacuum
horizon size (at three sigma). We conclude that very near-future data will have
the final word on bubble collisions in the CMB.
