  The inflationary scenario has become the paradigm of early universe
cosmology, and - in conjuction with ideas from superstring theory - has led to
speculations about an "inflationary multiverse". From a point of view of
phenomenology, the inflationary universe scenario has been very successful.
However, the scenario suffers from some conceptual problems, and thus it does
not (yet) have the status of a solid theory. There are alternative ideas for
the evolution of the very early universe which do not involve inflation but
which agree with most current cosmological observations as well as inflation
does. In this lecture I will outline the conceptual problems of inflation and
introduce two alternative pictures - the "matter bounce" and "string gas
cosmology", the latter being a realization of the "emergent universe" scenario
based on some key principles of superstring theory. I will demonstrate that
these two alternative pictures lead to the same predictions for the power
spectrum of the observed large-scale structure and for the angular power
spectrum of cosmic microwave background anisotropies as the inflationary
scenario, and I will mention predictions for future observations with which the
three scenarios can be observationally teased apart.
