Graviton self-energy from gravitons in cosmology

Although matter contributions to the graviton self-energy -i[(mu nu)Sigma(rho sigma)](x;x ') must be separately conserved on x(mu) and x '(mu), graviton contributions obey the weaker constraint of the Ward identity, which involves a divergence on both coordinates. On a general homogeneous and isotropic background this leads to just four structure functions for matter contributions but nine structure functions for graviton contributions. We propose a convenient parameterization for these nine structure functions. We also apply the formalism to explicit one loop computations of -i[(mu nu)Sigma(rho sigma)](x;x ') on de Sitter background, one of the contributions from a massless, minimally coupled scalar and the other for the contribution from gravitons in the simplest gauge. We also specialize the linearized, quantum-corrected Einstein equation to the graviton mode function and to the gravitational response to a point mass.