Hartree Approximation to the One Loop Quantum Gravitational Correction to the Graviton Mode Function on de Sitter

Abstract

We use the Hartree approximation to the Einstein equation on de Sitter background to solve for the one loop correction to the graviton mode function. This should give a reasonable approximation to how the ensemble of inflationary gravitons affects a single external graviton. At late times we find that the one loop correction to the plane wave mode function $u(\eta ,k)$ goes like $G{H}^2\ln (a)/a^2$, where $a$ is the inflationary scale factor. One consequence is that the one loop corrections to the "electric" components of the linearized Weyl tensor grow compared to the tree order result.

23 pages, uses LaTeX2e, version 2 expanded (by 7 pages) for publication to define the effective mode equation and compare the exact one loop result for it with the Hartree approximation

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• Excitation of Photons by Inflationary Gravitons
• Nonlocal Cosmology II --- Cosmic acceleration without fine tuning or dark energy
• The Hartree approximation in curved spacetimes revisited I: the effective potential in de Sitter
• Quantum Scalar Corrections to the Gravitational Potentials on de Sitter Background
• Large Logarithms from Quantum Gravitational Corrections to a Massless, Minimally Coupled Scalar on de Sitter
• A Caveat on Building Nonlocal Models of Cosmology
• Deducing Cosmological Observables from the S-matrix
• Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter II: kinetic-conformal cross terms
• Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter background
• Representing the Graviton Self-Energy on de Sitter Background
• Single Graviton Loop Contribution to the Self-Mass of a Massless, Conformally Coupled Scalar on de Sitter Background
• How Inflationary Gravitons Affect Gravitational Radiation
• Graviton Propagator in a 2-Parameter Family of de Sitter Breaking Gauges
• Graviton Self-Energy from Gravitons in Cosmology
• One-loop Graviton Corrections to Conformal Scalars on a de Sitter Background
• Causality Implies Inflationary Back-Reaction
• The Case for Nonlocal Modifications of Gravity
• A photon propagator on de Sitter in covariant gauges