Quadrupole formulae with cosmological constant: comparison

TL;DR

This paper compares three different approaches to generalize the quadrupole formula for gravitational radiation in de Sitter spacetime, showing they agree up to linear order in the cosmological constant.

Contribution

It demonstrates the equivalence of three distinct quadrupole formula generalizations in de Sitter space up to first order in the cosmological constant.

Findings

All three approaches yield consistent energy flux expressions up to linear order in b4;

The formulas are expressed in terms of mass and pressure quadrupole moments;

The approaches agree when gauge conditions and hypersurfaces are properly considered.

Abstract

We consider three different approaches (by Ashtekar, Bonga and Kesavan; Hoque and Virmani; and Dobkowski-Ry\l{}ko and Lewandowski) to investigate gravitational radiation produced by time changing matter source in de Sitter spacetime. All of them lead to generalizations of the quadrupole formula, however, due to different gauge conditions and choices of the hypersurfaces, across which the energy flux is computed, it is nontrivial to see that they all coincide, as one would expect from the symplectic theory. Each of the expressions for the radiated energy in the form of gravitational waves is expressed in terms of the mass and pressure quadrupole moments and written explicitly up to the linear order in $\sqrt{\Lambda}$, or equvalently in Hubble parameter $H$. It is shown that up to the first order all three of the generalizations of the quadrupole formula agree.