More On Cosmological Gravitational Waves And Their Memories

Abstract: 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.