Friedmann-Lema\^itre-Robertson-Walker cosmology through the lens of
  gravitoelectromagnetism
  Friedmann-Lema\^itre-Robertson-Walker cosmology is examined from the point of
view of gravitoelectromagnetism, in the approximation of spacetime regions
small in comparison with the Hubble radius. The usual Lorentz gauge is not
appropriate for this situation, while the Painlev\'e-Gullstrand gauge is rather
natural. Several non-trivial features and differences with respect to
"standard" asymptotically flat gravitoelectromagnetism are discussed.
