Gravitons from anomalous decay

Abstract

The decay rate of the neutral pion into two gravitons is calculated from the gravitational anomaly in the axial current. Although this decay rate is negligible relative to the decay rate of the neutral pion into two photons, the rate of decay into gravitons is proportional to the seventh power of the mass of the decaying particle, and to the square of the gravitational constant. The possibility that a particle of very large mass, associated with an axial current anomaly, was present in the early universe is considered. Such a particle would decay at a significant rate into gravitons. As these gravitons would not be thermaiized, they would result in a (potentially observable) nonthermal spectrum of gravitational waves present today. The peak frequency of this gravitational wave spectrum would be indicative of the mass of the decaying particle. Alternatively, if the gravitational constant were large at early times, then the gravitational decay of the pion would be significant in the early universe, giving rise to a nonthermal gravitational wave spectrum.