  Inflation creates large-scale cosmological density perturbations that are
characterized by an isotropic, homogeneous, and Gaussian random distribution
about a locally flat background. Even in a flat universe, the spatial curvature
measured within one Hubble volume receives contributions from long wavelength
perturbations, and will not in general be zero. These same perturbations
determine the Cosmic Microwave Background (CMB) temperature fluctuations, which
are O(10^-5). Consequently, the low-l multipole moments in the CMB temperature
map predict the value of the measured spatial curvature \Omega_k. On this basis
we argue that a measurement of |\Omega_k| > 10^-4 would rule out slow-roll
eternal inflation in our past with high confidence, while a measurement of
\Omega_k < -10^-4 (which is positive curvature, a locally closed universe)
rules out false-vacuum eternal inflation as well, at the same confidence level.
In other words, negative curvature (a locally open universe) is consistent with
false-vacuum eternal inflation but not with slow-roll eternal inflation, and
positive curvature falsifies both. Near-future experiments will dramatically
extend the sensitivity of \Omega_k measurements and constitute a sharp test of
these predictions.
