262 Inflation I: homogeneous limit
Fig. 5.8.de Sitter space and the lower border for the flat, open or closed Friedmann universes
(Figure 5.8), where the difference between the hypersurfaces of constant time for
flat, open or closed cases is negligibly small. After a graceful exit we obtain a very
large domain of the Friedmann universe with incredibly small flatness and this
domain covers all present observable scales. The global structure of the universe
on scales much larger than the present horizon is not relevant for an observer−at
least not for the next 100 billion years. In Part II we will see that the issue of the
global structure is complicated by quantum fluctuations. These fluctuations are am-
plified during inflation and as a result the hypersurface of transition has “wrinkles.”
The wrinkles are rather small on scales corresponding to the observable universe
but they become huge on the very large scales. Hence, globally the universe is
very different from the Friedmann space and the question about the spatial curva-
ture of the whole universe no longer makes sense. It also follows that the global
properties of an exact de Sitter solution have no relevance for the real physical
universe.