A New Gravitational Action for the Trace Anomaly

I will discuss the question of building a local diff-invariant effective gravitational action for the trace anomaly. General Relativity (GR) combined with the existing action for the trace anomaly is an inconsistent low energy effective field theory. This issue is addressed by extending GR into a certain scalar-tensor theory, which preserves the GR trace anomaly equation, up to higher order corrections. The extension introduces a new mass scale – assumed to be below the Planck scale – that governs four high dimensional terms in a local diff-invariant trace anomaly action. Such terms can be kept, while an infinite number of Planck-suppressed invariants are neglected. The resulting theory maintains two derivative equations of motion. In a certain approximation it reduces to the conformal Gallileon, which could have physical consequences.