More On Cosmological Gravitational Waves And Their Memories
  We extend recent theoretical results on the propagation of linear
gravitational waves (GWs), including their associated memories, in spatially
flat Friedmann--Lema\^{i}tre--Robertson--Walker (FLRW) universes, for all
spacetime dimensions higher than 3. By specializing to a cosmology driven by a
perfect fluid with a constant equation-of-state $w$ -- conformal re-scaling,
dimension-reduction and Nariai's ansatz may then be exploited to obtain
analytic expressions for the graviton and photon Green's functions, allowing
their causal structure to be elucidated. When $0 < w \leq 1$, the
gauge-invariant scalar mode admits wave solutions, and like its tensor
counterpart, likely contributes to the tidal squeezing and stretching of the
space around a GW detector. In addition, scalar GWs in 4D radiation dominated
universes -- like tensor GWs in 4D matter dominated ones -- appear to yield a
tail signal that does not decay with increasing spatial distance from the
source. We then solve electromagnetism in the same cosmologies, and point out a
tail-induced electric memory effect. Finally, in even dimensional Minkowski
backgrounds higher than 2, we make a brief but explicit comparison between the
linear GW memory generated by point masses scattering off each other on unbound
trajectories and the linear Yang-Mills memory generated by color point charges
doing the same -- and point out how there is a "double copy" relation between
the two.
