Gravitational wave memory in de Sitter spacetime

TL;DR

This work investigates gravitational wave memory in an expanding universe by focusing on a de Sitter background and employing gauge-invariant Weyl-tensor perturbations in a conformally flat FLRW framework. It shows memory behavior parallels the flat-space case, with two memory channels—ordinary memory from changes in the radial electric Weyl component and null memory from energy radiated per solid angle—where the null contribution acquires a cosmological redshift enhancement. The memory is encoded via a scalar potential on the sphere, linking $\Delta P$, the radiated energy flux $F$, and integrated shear-like quantities; observational implications are discussed in terms of luminosity distance and redshift. The authors also outline how to generalize to dust+$\Lambda$, noting potential shear couplings and that geometric optics arguments may render them subdominant, with ongoing work to clarify this regime.

Abstract

We examine gravitational wave memory in the case where sources and detector are in an expanding cosmology. For simplicity, we treat the case where the cosmology is de Sitter spacetime, and discuss the possibility of generalizing our results to the case of a more realistic cosmology. We find results very similar to those of gravitational wave memory in an asymptotically flat spacetime, but with the magnitude of the effect multiplied by a redshift factor.