  The IKKT matrix model yields an emergent space-time. We further develop these
ideas and give a proposal for an emergent metric. Based on previous numerical
studies of this model, we provide evidence that the emergent space-time is
continuous and infinite in extent, both in space and in time, and that the
metric is spatially flat. The time evolution describes the transition from a
string-theoretic emergent phase to a phase in which the $SO(9)$ symmetry of the
model is spontaneously broken to $SO(6) \times SO(3)$, with three dimensions of
space expanding, becoming classical and at later times evolving like in a
radiation-dominated universe, and the remaining six dimensions of space
stabilized at the string scale. We speculate on how this analysis can be
extended to yield an early universe cosmology which, in addition to the
above-mentioned properties, also leads to a roughly scale-invariant spectrum of
cosmological fluctuations and gravitational waves.
