  Inflationary theory predicts that the observable Universe should be very
close to flat, with a spatial-curvature parameter |Omega_K| < 10^-4. The WMAP
satellite currently constrains |Omega_K| < 0.01, and the Planck satellite will
be sensitive to values near 10^-3. Suppose that Planck were to find Omega_K to
be non-zero at this level. Would this necessarily be a serious problem for
inflation? We argue that an apparent departure from flatness could be due
either to a local (wavelength comparable to the observable horizon)
inhomogeneity, or a truly superhorizon departure from flatness. If there is a
local inhomogeneity, then secondary CMB anisotropies distort the CMB frequency
spectrum at a level potentially detectable by a next-generation experiment. We
discuss how these spectral distortions would complement constraints on the
Grishchuk-Zel'dovich effect from the CMB power spectrum at large angular scales
in discovering the source of the departure from flatness.
