  I review a class of exact string backgrounds, which appear in hierarchies,
where the boundary of the target space of an exact sigma model is itself the
target space of another exact model. From the worldsheet viewpoint this is due
to the existence of (1,1) operators based on parafermions. From the target
space side, it is reminiscent of the structure of maximally symmetric
Friedmann-Robertson-Walker cosmological solutions, with broken homogeneity
though. Cosmological evolution in this framework raises again the question of
the nature of time in string theory.
