Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2012-03-20
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Scientific paper
The propagation of gravitational waves in an asymptotically de-Sitter space, can be analyzed by using two different points of view. The first one and the most evident is by studying the propagation of the field $(h)$ around the de-Sitter background. The second one is by expanding the perturbation around Minkowski and introducing the effects of the Cosmological Constant $\Lambda$ as an additional source. In this way the full solution of the field $h$ has two parts. One corresponds to the standard plane wave solution and the other corresponds to an additional contribution due to $\Lambda$. This can be done if the condition $|h| << 1$ is always accomplished for both solutions, only in such a way the concept of gravitational wave makes sense. Both points of views have already been analyzed in the literature. When the propagation of the wave is studied around Minkowski, the simplest way to do it is by using the De-donder gauge. Other gauge, called the $\Lambda$ gauge has been used recently in order to analyze the propagation of gravitational waves in an asymptotically de-Sitter space by using the expansion around Minkowski. It is already known that the inclusion of $\Lambda$ produces some modifcations on the local observables. In this paper we demonstrate: 1). The same results are obtained by working with the Lambda gauge or the de-Donder gauge. It means that the results are physically relevant and not only a coordinate effect. 2). The so-called critical distance is just equivalent to the standard condition $r\approx\frac{\lambda}{h}$. This is just the condition that must be satisfied if we want the gravitational wave concept to make sense. 3). In the $\Lambda$ gauge, it is possible to show explicitly that we still have two physically relevant polarization components with the appropiate behavior under rotation.
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