Anomaly-free scale symmetry and gravity

In this Letter, we address the question of whether conformal invariance can be considered as a global symmetry theory fundamental interactions. To describe Nature, must contain mechanism spontaneous breaking scale symmetry. Besides that, include gravity, whereas all known extensions to curved space-time suffer from Weyl anomaly. We show that made free quantum anomaly only in flat space. The presence gravity would reduce group only. discuss how effective Lagrangian respecting used for description particle phenomenology and cosmology.