  Matrix models of Yang-Mills type lead to an emergent gravity theory, which
may not require fine-tuning of a cosmological constant. We find cosmological
solutions of Friedmann-Robertson-Walker type. They generically have a big
bounce, and an early inflation-like phase with graceful exit. The mechanism is
purely geometrical, no ad-hoc scalar fields are introduced. The solutions are
stabilized through vacuum fluctuations and are thus compatible with quantum
mechanics. This leads to a Milne-like universe after inflation, which appears
to be in remarkably good agreement with observation and may provide an
alternative to standard cosmology.
