  Very small mean curvature is a robust prediction of inflation worth rigorous
checking. Since current constraints are derived from determinations of the
angular-diameter distance to the CMB last-scattering surface, which is also
affected by dark energy, they are limited by our understanding of the dark
energy. Measurements of luminosity or angular-diameter distances to redshifts
in the matter-dominated era can greatly reduce this uncertainty. With a one
percent measurement of the distance to z=3, combined with the CMB data expected
from Planck, one can achieve sigma(\Omega_k h^2) \sim 10^{-3}. A non-zero
detection at this level would be evidence against inflation or for unusually
large curvature fluctuations on super-Hubble scales.
