The Standard Picture: In standard inflaton potentials a high degree of adjustment is required to achieve a suitably small amplitude for the density perturbations. It turns out that this adjustment also drives the overall time of inflation far (often exponentially) beyond the ``minimal'' 60 e-foldings. As a result, the total curvature of the Universe is precisely zero today in inflationary cosmologies, at least as foreseeable observations are concerned. Any evidence for a non-zero curvature at the precisions of realistic experiments will overturn the standard inflationary picture. The current data is consistent with a flat Universe as illustrated in Fig. 11.
Figure 11. This is Fig. 4 from . This shows that the Maxima and Supernova data consistent with a flat Universe (indicated by the diagonal m + = 1 line).
Exotic variations: The possibility that an open Universe could emerge at the end of inflation has been considered for some time [15, 16]. For example in  a period of ordinary old inflation ends by bubble nucleation, and there is subsequently a brief period of new inflation inside the bubble. The degree of openness is controlled by the shape of the inflaton potential, which determines the initial field values inside the bubble and the duration of inflation afterwards. The open inflation models suggest an interesting direction of study if the universe turns out to be open, but they also represent a picture that is radically different from the standard inflationary one.