Gravitational wave memory in dS_4+2n and 4D cosmology

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 (a²η_ϵμ dx^ϵ dx^μ)-after the source has ceased and the primary GW train has passedamounts to a spacetime constant shift in the flat metric proportional to the difference between the TT parts of the sources final and initial mass quadrupole moments. As a byproduct, we present solutions to Einsteins 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 4D cosmological results of Chu (2015 Phys. Rev. D 92 124038), which in turn preceded complementary work by Bieri et al (2015 arXiv:1509.01296) and by Kehagias and Riotto (2016 arXiv:1602.02653).