Gravitational Waves from Compact Sources in de Sitter Background

TL;DR

This paper investigates how a positive cosmological constant affects gravitational waves from compact sources, providing first-order corrections in de Sitter space and introducing a gauge-invariant polarization measure.

Contribution

It offers the first detailed calculation of gravitational radiation corrections in de Sitter background using Fermi normal coordinates and introduces a new gauge-invariant polarization scalar.

Findings

First-order corrections in $\Lambda$ to gravitational fields are computed.

The deviation scalar captures polarization information in de Sitter space.

Differences between static and Poincare patches are analyzed.

Abstract

The concordance model of cosmology favours a universe with a tiny positive cosmological constant. A tiniest positive constant curvature, profoundly alters the asymptotic structure, forcing a re-look at a theory of gravitational radiation. Even for compact astrophysical sources, the intuition from Minkowski background is challenged at every step. Nevertheless, at least for candidate sources such as compact binaries, it is possible to quantify influence of the cosmological constant, as small corrections to the leading order Minkowski background results. Employing suitably chosen Fermi normal coordinates in the static patch of the de Sitter background, we compute the field due to a compact source to first order in $\Lambda$. For contrast, we also present the field in the Poincare patch where the leading correction is in $\sqrt{\Lambda}$. We introduce a gauge invariant quantity, {\em deviation scalar}, containing polarization information and compute it in both charts for a comparison.