Gravitational wave memory in $Λ$CDM cosmology

TL;DR

The paper develops a gauge-invariant, short-wavelength perturbation framework to compute gravitational wave memory in a ΛCDM universe, dividing propagation into a flat-wave zone and a cosmological FLRW zone. It shows that the memory amplitude is enhanced by a redshift factor and a lensing magnification, with inhomogeneities introducing a Sachs–Wolfe–type magnification ζ that can further modify the memory in the cosmological zone. The main result is that the cosmological memory relates to the flat-space memory via m^{(2)}_{AB} = (1+z)(1+ζ) m^{(1)}_{AB}, reducing to the familiar (1+z) scaling in a homogeneous background. These findings have practical implications for interpreting memory signals with current and future detectors (LIGO/Virgo, ET, CE, LISA, and pulsar timing arrays), where redshift and lensing corrections will be essential for detecting and mapping memory across cosmological distances.

Abstract

We examine gravitational wave memory in the case where sources and detector are in a $Λ$CDM cosmology. We consider the case where the universe can be highly inhomogeneous, but the gravitatational radiation is treated in the short wavelength approximation. We find results very similar to those of gravitational wave memory in an asymptotically flat spacetime; however, the overall magnitude of the memory effect is enhanced by a redshift-dependent factor. In addition, we find the memory can be affected by lensing.