Transformation Properties of Linearized de Sitter Gravity Solutions

TL;DR

This paper examines how linearized quantum gravity solutions in de Sitter space transform under de Sitter group actions, demonstrating their closure under these transformations with appropriate gauge adjustments.

Contribution

It explicitly analyzes the transformation properties of linearized de Sitter gravity solutions, showing their invariance under the de Sitter group with gauge compensation.

Findings

Solutions are closed under de Sitter transformations.

A compensating gauge transformation is necessary to maintain the gauge.

Transformations preserve the form of solutions within the gauge.

Abstract

The effect of de Sitter transformations on Tsamis and Woodard's solutions to the linearized gauge fixed equations of motion of quantum gravity in a de Sitter space background is worked out explicitly. It is shown that these solutions are closed under the transformations of the de Sitter group. To do this it is necessary to use a compensating gauge transformation to return the transformed solution to the original gauge.