Cosmology and the fate of dilatation symmetry

We discuss the cosmological constant problem in the light of dilatation symmetry and its possible anomaly. For dilatation symmetric quantum theories realistic asymptotic cosmology is obtained provided the effective potential has a nontrivial minimum. For theories with dilatation anomaly one needs as a nontrivial ``cosmon condition'' that the energy-momentum tensor in the vacuum is purely anomalous. Such a condition is related to the short distance renormalization group behaviour of the fundamental theory. Observable deviations from the standard hot big bang cosmology are possible.