C. Wetterich discusses the cosmological constant problem in the context of dilatation symmetry and its possible anomaly. He argues that for dilatation symmetric quantum theories, realistic asymptotic cosmology is achieved if the effective potential has a non-trivial minimum. In theories with dilatation anomalies, a non-trivial "cosmon condition" is required, where the energy-momentum tensor in the vacuum is purely anomalous. This condition is related to the short-distance renormalization group behavior of the fundamental theory. Observable deviations from the standard hot big bang cosmology are possible. The paper explores models without mass scales, where the effective potential depends only on the ratio of scalar fields. It discusses dilatation anomalies and the cosmon condition, which are necessary for realistic cosmology. The cosmon condition is connected to the short-distance behavior of the underlying fundamental theory. The paper also examines the renormalization group equation for the cosmological "constant" and its implications for cosmology with time variation of the cosmological "constant". It concludes that the fate of dilatation symmetry is closely related to the cosmological constant problem. The study of cosmologies with a dynamical Planck mass is connected to the fate of dilatation symmetry, and the paper is a logical continuation of previous work. The paper emphasizes the importance of the cosmon condition and the role of the dilatation anomaly in determining the behavior of the effective potential and the cosmological constant. The results show that realistic cosmology can be achieved if the anomalous dimension A is within a certain range. The paper concludes with a discussion of the cosmological constant problem and the implications of the cosmon condition for realistic cosmology.C. Wetterich discusses the cosmological constant problem in the context of dilatation symmetry and its possible anomaly. He argues that for dilatation symmetric quantum theories, realistic asymptotic cosmology is achieved if the effective potential has a non-trivial minimum. In theories with dilatation anomalies, a non-trivial "cosmon condition" is required, where the energy-momentum tensor in the vacuum is purely anomalous. This condition is related to the short-distance renormalization group behavior of the fundamental theory. Observable deviations from the standard hot big bang cosmology are possible. The paper explores models without mass scales, where the effective potential depends only on the ratio of scalar fields. It discusses dilatation anomalies and the cosmon condition, which are necessary for realistic cosmology. The cosmon condition is connected to the short-distance behavior of the underlying fundamental theory. The paper also examines the renormalization group equation for the cosmological "constant" and its implications for cosmology with time variation of the cosmological "constant". It concludes that the fate of dilatation symmetry is closely related to the cosmological constant problem. The study of cosmologies with a dynamical Planck mass is connected to the fate of dilatation symmetry, and the paper is a logical continuation of previous work. The paper emphasizes the importance of the cosmon condition and the role of the dilatation anomaly in determining the behavior of the effective potential and the cosmological constant. The results show that realistic cosmology can be achieved if the anomalous dimension A is within a certain range. The paper concludes with a discussion of the cosmological constant problem and the implications of the cosmon condition for realistic cosmology.