Factorization and polarization in linearized gravity

We investigate all the four-body graviton interaction processes: gX{→}{γ}X, gX{→}gX, and gg{→}gg with X as an elementary particle of spin less than 2 in the context of linearized gravity except the spin-3/2 case. We show explicitly that gravitational gauge invariance and Lorentz invariance cause every four-body graviton scattering amplitude to be factorized. We explore the implications of this factorization property by investigating polarization effects through the covariant density matrix formalism in each four-body graviton scattering process.