Graviton Self-Energy from Gravitons in Cosmology

Abstract

Although matter contributions to the graviton self-energy $-i[\mbox{}^{μν} Σ^{ρσ}](x;x')$ must be separately conserved on $x^{\hat{I}}¼$ and ${x^{\prime }}^{\hat{I}}¼$, 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 $-i[\mbox{}^{μν} Σ^{ρσ}](x;x')$ 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.

42 pages, 2 figures, 10 tables, uses LaTeX 2e. This paper is dedicated to Stanley Deser on the occasion of his 90th birthday. Version 2 (48 pages) revised for publication with extensive discussion of gauge dependence and of the procedure for generalizing the noncoincident 1996 graviton self-energy to a fully renormalized result