Memories from the distant past: Nonlinear effect due to gravitational waves in an expanding universe

In this essay, we investigate the gravitational wave memory effect in expanding universes, specifically in de Sitter and [Formula: see text]CDM spacetime and envisage their observational implications. We employ conformal compactification to define asymptotic structures in expanding spacetimes. We apply the Bondi–Sachs formalism to derive modified mass-loss formulas. We also apply perturbative expansions within the Einstein-fluid equations for matter coupling in [Formula: see text]CDM models. Importantly, we observe that cosmic expansion amplifies gravitational wave memory, with a modified Bondi mass-loss formula incorporating a redshift-dependent factor enhancing energy flux. These effects suggest detectable memory signals from high-redshift sources.