Scalar Contribution to the Graviton Self-Energy during Inflation

Abstract

We use dimensional regularization to evaluate the one loop contribution to the graviton self-energy from a massless, minimally coupled scalar on a locally de Sitter background. For noncoincident points our result agrees with the stress tensor correlators obtained recently by Perez-Nadal, Roura and Verdaguer. We absorb the ultraviolet divergences using the $R^2$ and $C^2$ counterterms first derived by 't Hooft and Veltman, and we take the $D=4$ limit of the finite remainder. The renormalized result is expressed as the sum of two transverse, 4th order differential operators acting on nonlocal, de Sitter invariant structure functions. In this form it can be used to quantum-correct the linearized Einstein equations so that one can study how the inflationary production of infrared scalars affects the propagation of dynamical gravitons and the force of gravity.

54pages

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• Nonlocal Cosmology II --- Cosmic acceleration without fine tuning or dark energy
• Large Logarithms from Quantum Gravitational Corrections to a Massless, Minimally Coupled Scalar on de Sitter
• Covariant Vacuum Polarizations on de Sitter Background
• Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter background
• How Inflationary Gravitons Affect the Force of Gravity
• Graviton Self-Energy from Gravitons in Cosmology
• Summing Gravitational Effects from Loops of Inflationary Scalars
• Symmetry breaking in de Sitter: a stochastic effective theory approach
• Appearances are deceptive: Can graviton have a mass?
• The Third Structure Function
• Backreaction of particle production on physical gravitons in the de Sitter space