  Symmetries play an interesting role in cosmology. They are useful in
characterizing the cosmological perturbations generated during inflation and
lead to consistency relations involving the soft limit of the statistical
correlators of large-scale structure dark matter and galaxies overdensities. On
the other hand, in observational cosmology the carriers of the information
about these large-scale statistical distributions are light rays traveling on
null geodesics. Motivated by this simple consideration, we study the structure
of null infinity and the associated BMS symmetry in a cosmological setting. For
decelerating Friedmann-Robertson-Walker backgrounds, for which future null
infinity exists, we find that the BMS transformations which leaves the
asymptotic metric invariant to leading order. Contrary to the asymptotic flat
case, the BMS transformations in cosmology generate Goldstone modes
corresponding to both scalar and tensor degrees of freedom which may exist at
null infinity and perturb the asymptotic data. Therefore, BMS transformations
generate physically inequivalent vacua as they populate the universe at null
infinity with these physical degrees of freedom. We also discuss the
gravitational memory effect when cosmological expansion is taken into account.
In this case, there are extra contribution to the gravitational memory due to
the tail of the retarded Green functions which are supported not only on the
light-cone, but also in its interior. The gravitational memory effect can be
understood also from an asymptotic point of view as a transition among
cosmological BMS-related vacua.
