Fermi coordinates, simultaneity, and expanding space in Robertson-Walker
  cosmologies
  Explicit Fermi coordinates are given for geodesic observers comoving with the
Hubble flow in expanding Robertson-Walker spacetimes, along with exact
expressions for the metric tensors in Fermi coordinates. For the case of non
inflationary cosmologies, it is shown that Fermi coordinate charts are global,
and space-time is foliated by space slices of constant Fermi (proper) time that
have finite extent. A universal upper bound for the proper radius of any leaf
of the foliation, i.e., for the proper radius of the spatial universe at any
fixed time of the geodesic observer, is given. A general expression is derived
for the geometrically defined Fermi relative velocity of a test particle (e.g.
a galaxy) comoving with the Hubble flow away from the observer. Least upper
bounds of superluminal recessional Fermi velocities are given for spacetimes
whose scale factors follow power laws, including matter-dominated and
radiation-dominated cosmologies. Exact expressions for the proper radius of any
leaf of the foliation for this same class of spacetimes are given. It is shown
that the radii increase linearly with proper time of the observer moving with
the Hubble flow. These results are applied to particular cosmological models.
