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.