Graviton self-energy from gravitons in cosmology*

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Abstract
Although matter contributions to the graviton self-energy − i [ Σ ρ σ μ ν ] ( x ; x ′ ) must be separately conserved on x μ and x ′ μ , 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 [ Σ ρ σ μ ν ] ( 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.
Funding Information
  • European Union’s Seventh Framework Programme (316165)
  • National Science Foundation (PHY 1506513)
  • European Union’s Horizon 2020 Programme (669288-SM-GRAV-ERC-2014-ADG)

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