Power radiated by a binary system in a de Sitter universe

Abstract

Gravitational waves emitted by high redshift sources propagate through various epochs of the Universe including the current era of measurable, accelerated expansion. Historically, the calculation of gravitational wave power on cosmological backgrounds is based on various simplifications, including a 1/r-expansion and the use of an algebraic projection to retrieve the radiative degrees of freedom. On a de Sitter spacetime, recent work has demonstrated that many of these calculational techniques and approximations do not apply. Here we calculate the power emitted by a binary system on a de Sitter background using techniques tailored to de Sitter spacetime. The common expression for the power radiated by this source in an FLRW spacetime, calculated using far wavezone techniques, gives the same expression as the late time expansion specialized to the de Sitter background in the high-frequency approximation. * bpb165@psu.edu

On propagation of energy flux in de Sitter spacetime

“…In fact, it appears to work better than expected. In the context of the power radiated by a spatially compact circular binary system analysed in [12,13] the difference does not seem to matter.…”

“…Hence, χ TT ij is best regarded as the physical component of the field χ ij . Given a tensor χ ij , in general it is highly non-trivial to extract χ TT ij ; see [12] for an explicit example. In the context of gravitational waves, another conceptually distinct notion of transverse-traceless tensors is often used in the literature.…”

“…For a detailed discussion of the differences between these two notions see [17,18]. For asymptotically flat space-times the two notions match only at null infinity I + [18,12]. The tt-projection is well tailored to the 1/r expansion commonly used for asymptotically flat spacetimes.…”

“…This is the sense in which propagation of energy flux is sharp in de Sitter spacetime. See also [10,12] for related comments.…”

“…Subsequently, several authors have contributed to the development of the subject [9,10,11,12,13]. The primary aim of this work is to expand on some of these studies, in particular on some aspects of [9,10], and to clarify their relation to [6,8].…”