  We study cosmological solutions of the IKKT model with $k=-1$ FLWR geometry,
taking into account one-loop corrections. A previously discussed covariant
quantum spacetime is found to be stabilized through one-loop effects at early
times, without adding a mass term to the model. At late times, this background
is modified and goes through a period of acceleration, before settling down to
a coasting FLRW geometry with scale parameter $a(t) \sim t$. This is
qualitatively close to observation without any fine-tuning, irrespective of the
detailed matter content of the universe.
