Graviton Self-Energy from Gravitons in Cosmology

TL;DR

This paper analyzes the structure functions of graviton self-energy in cosmology, proposing a parameterization and computing one-loop contributions from scalars and gravitons on de Sitter background, with implications for quantum-corrected Einstein equations.

Contribution

It introduces a new parameterization for graviton self-energy structure functions and performs explicit one-loop calculations in a cosmological setting.

Findings

Nine structure functions for graviton contributions identified

Explicit one-loop results for scalar and graviton contributions obtained

Implications for quantum-corrected Einstein equations discussed

Abstract

Although matter contributions to the graviton self-energy $-i[\mbox{}^{\mu\nu} \Sigma^{\rho\sigma}](x;x')$ 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 $-i[\mbox{}^{\mu\nu} \Sigma^{\rho\sigma}](x;x')$ 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.