  Cosmology is most typically analyzed using standard co-moving coordinates, in
which the galaxies are (on average, up to presumably small peculiar velocities)
"at rest", while "space" is expanding. But this is merely a specific coordinate
choice; and it is important to realise that for certain purposes other,
(sometimes radically different) coordinate choices might also prove useful and
informative, but without changing the underlying physics. Specifically, herein
we shall consider the k=0 spatially flat FLRW cosmology but in
Painleve-Gullstrand coordinates -- these coordinates are very explicitly not
co-moving: "space" is now no longer expanding, although the distance between
galaxies is still certainly increasing. Working in these Painleve-Gullstrand
coordinates provides an alternate viewpoint on standard cosmology, and the
symmetries thereof, and also makes it somewhat easier to handle cosmological
horizons. With a longer view, we hope that investigating these
Painleve-Gullstrand coordinates might eventually provide a better framework for
understanding large deviations from idealized FLRW spacetimes. We illustrate
these issues with a careful look at the Kottler and McVittie spacetimes.
