Macroscopic Effects of the Quantum Conformal Anomaly: Scalar Gravitational Waves, Black Holes, and Dark Energy

Abstract

In the second lecture, I will extend the previous discussion to gravity, and show that the conformal trace anomaly must play a special role in the effective field theory of low energy gravity. Classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields, which implies the existence of a new long range massless scalar degree of freedom, not present in the classical Einstein theory, that contributes to gravitational scattering processes and has long range gravitational effects. Similar to the axial anomaly, the local form of the effective action associated with the conformal anomaly is expressible in terms of a dynamical scalar field that couples to the conformal factor of the spacetime metric, allowing it to propagate over macroscopic distances. Among the significant implications of this effective field theory of gravity are the prediction of scalar gravitational wave solutions—a spin-0 breather mode— in addition to the transversely polarized tensor waves of the classical Einstein theory. Astrophysical sources for scalar gravitational waves are considered, with the excited gluonic condensates in the interiors of neutron stars in merger events with other compact objects likely to provide the strongest burst signals. The conformal anomaly also implies generically large quantum back reaction effects and conformal correlators in the vicinity of black hole horizons which are relevant to the formation of a non-singular interior, as well as an additional scalar degree of freedom in cosmology, providing a theoretical foundation for dynamical dark energy.