Cosmological measurements of the average spatial curvature of the spacetime metric are one of only a handful of methods available for testing the inflationary paradigm for the early universe. Current observations are consistent with the inflationary prediction of a nearly flat universe. However, the precision of curvature measurements is only at the percent level at best (e.g., Eisenstein et al., 2005; Komatsu et al., 2009), whereas the expected level of curvature in standard inflationary scenarios is generally much smaller.