An SZ-Like Effect on the Stochastic Gravitational Wave Background

The stochastic gravitational wave background is the conglomeration of unresolved gravitational waves signals from the early universe and astrophysical sources. By deriving the gravitational analog to the Kompaneets equation we establish that much like the cosmic microwave background, inverse Compton scattering will induce small distortions in the intensity spectrum of the stochastic background. We then show that when these spectral distortions can be attributed to the dark matter in the early universe, one can infer the spin of the dark matter particle.