Graviton Propagation and Vacuum Polarization in Curved Space

TL;DR

This paper investigates how vacuum polarization from massive scalar particles affects graviton propagation in curved spacetime, revealing an effective refractive index with real and imaginary parts that influence graviton behavior.

Contribution

It provides a novel analysis of graviton vacuum polarization effects in curved space, deriving an effective refractive index in a large mass and WKB limit.

Findings

Refractive index has both real and imaginary components.

Imaginary part affects graviton wavefunction normalization.

Real part increases logarithmically with frequency under null energy condition.

Abstract

The effects of vacuum polarization arising from loops of massive scalar particles on graviton propagation in curved space are considered. Physically, they are due to curvature induced tidal forces acting on the cloud of virtual scalar particles surrounding the graviton. The effects are tractable in a WKB and large mass limit and the results can be written as an effective refractive index for the graviton modes with both a real and imaginary part. The imaginary part of the refractive index is a curvature induced contribution to the wavefunction renormalization of the graviton in real affine time and can have the effect of dressing or un-dressing the graviton. The real part of the refractive index increases logarithmically at high frequency as long as the null energy condition is satisfied by the background.