  We present here the transformations required to recast the Robertson-Walker
metric and Friedmann-Robertson-Walker equations in terms of observer-dependent
coordinates for several commonly assumed cosmologies. The overriding motivation
is the derivation of explicit expressions for the radius R_h of our cosmic
horizon in terms of measurable quantities for each of the cases we consider. We
show that the cosmological time dt diverges for any finite interval ds
associated with a process at R -> R_h, which therefore represents a physical
limit to our observations. This is a key component required for a complete
interpretation of the data, particularly as they pertain to the nature of dark
energy. With these results, we affirm the conclusion drawn in our earlier work
that the identification of dark energy as a cosmological constant does not
appear to be consistent with the data.
