  Many astrophysical and cosmological observations consistently indicate that
the universe is currently accelerating. Despite many possible explanations, the
exact cause of this acceleration remains unknown. Therefore, additional
observational probes are necessary to pinpoint the cause. Gravitational waves
(GWs) have the potential to unravel some of the unresolved mysteries in
cosmology. In this work, we highlight the potential utility of gravitational
wave memory as a tool to identify the cause of this acceleration. We evaluate
cosmological memory as a particular case of the master equation for GW memory
in Locally Rotationally Symmetric type II spacetimes. Unlike the previous
works, the master equation for GW memory contains non-linear dependence of the
background quantities. Hence, even though the successive GWs generated are
smaller than their predecessors, we demonstrate that their cumulative effect
over cosmological time leads to observable signatures, akin to the growth of
density perturbations resulting in large-scale structures. Finally, we show
that the GW memory exhibits distinct signatures between accelerated and
decelerated universes, potentially enabling the identification of the
transition redshift from a matter-dominated to a dark-energy-dominated
universe.
