Linearized gravitational waves in de Sitter space-time

TL;DR

This paper clarifies the proper truncation of linearized gravitational waves in de Sitter space-time, resolving inconsistencies related to gauge conditions and asymptotic forms.

Contribution

It identifies the correct quadrupolar truncation method that avoids logarithmic terms in the Bondi-Sachs form, ensuring consistent solutions.

Findings

Proper quadrupolar truncation avoids logarithmic terms.

Gauge conditions and homogeneous solutions resolve inconsistencies.

Clarifies the asymptotic behavior of gravitational waves in de Sitter space.

Abstract

This is a brief note on a recently flagged issue \cite{CHK} regarding the precise characterization of quadrupolar truncation of the linearized gravitational waves in de Sitter space-time. An apparent inconsistency was noted while transforming the linearized solution truncated to quadrupolar contribution to the Bondi-Sachs form. A consistent truncation was identified as one where the transformation of the truncated solution does not generate logarithmic terms inadmissible in the Bondi-Sachs asymptotic form. I point out the role of the gauge conditions and the solution of the homogeneous equation in obviating the apparent inconsistency issue.