Gravitational wave memory in dS _{4+2 n} and 4D cosmology

Abstract

We argue that massless gravitons in all even dimensional de Sitter (dS) spacetimes higher than two admit a linear memory effect arising from their propagation inside the null cone. Assume that gravitational waves (GWs) are being generated by an isolated source, and over only a finite period of time η i ≤ η ≤ η f . Outside of this time interval, suppose the shear-stress of the GW source becomes negligible relative to its energy-momentum and its mass quadrupole moments settle to static values. We then demonstrate, the transverse-traceless (TT) GW contribution to the perturbation of any dS 4+2n written in a conformally flat form (a 2 η µν dx µ dx ν ) -after the source has ceased and the primary GW train has passed -amounts to a spacetime constant shift in the flat metric proportional to the difference between the TT parts of the source's final and initial mass quadrupole moments. As a byproduct, we present solutions to Einstein's equations linearized about de Sitter backgrounds of all dimensions greater than three. We then point out there is a similar but approximate tail induced linear GW memory effect in 4D matter dominated universes. Our work here serves to improve upon and extend the

Memory in de Sitter space and Bondi-Metzner-Sachs-like supertranslations

“…The result agrees with that of other authors [18,19,20,21,22]. The argument of the zero mode is almost the same as that for the flat background.…”

“…In light of these experimental prospects, it is natural to ask whether the above triangular relation applies to an accelerating universe like ours as well. The effect of gravitational memory in Minkowski spacetime was derived long ago [15,16,17], and has since been generalized to de Sitter spacetime or FLRW universes by several groups [18,19,20,21,22,23]. Our derivation of the memory effect in de Sitter space differs from that of previous works in several respects, most notably, the emphasis on its relation with spacetime diffeomorphisms.…”

“…We also assume that the typical frequency from the source is much larger than the Hubble scale H, and neglect the "tail" effect [18,21] in the following discussion.…”

“…It is instructive to compare our approach with previous investigations on the memory effect in de Sitter spacetime [18,19,21,22,23] . Our definition of the memory effect is different from that in Refs [18,21,23], as the effect of tidal force is naturally excluded in our analysis.…”

“…Our definition of the memory effect is different from that in Refs [18,21,23], as the effect of tidal force is naturally excluded in our analysis. In contrast to Ref.…”