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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 Rh 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 → Rh, 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. [ABSTRACT FROM AUTHOR]

Within the context of standard cosmology, an accelerating universe requires the presence of a third "dark" component of energy, beyond matter and radiation. The available data, however, are still deemed insufficient to distinguish between an evolving dark energy component and the simplest model of a time-independent cosmological constant. In this paper, we examine the cosmological expansion in terms of observer-dependent coordinates, in addition to the more conventional comoving coordinates. This procedure explicitly reveals the role played by the radius Rh of our cosmic horizon in the interrogation of the data. (In Rindler's notation, Rh coincides with the "event horizon" in the case of de Sitter, but changes in time for other cosmologies that also contain matter and/or radiation.) With this approach, we show that the interpretation of dark energy as a cosmological constant is clearly disfavored by the observations. Within the framework of standard Friedmann–Robertson–Walker cosmology, we derive an equation describing the evolution of Rh, and solve it using the WMAP and Type Ia supernova data. In particular, we consider the meaning of the observed equality (or near-equality) Rh(t0) ≅ ct0, where t0 is the age of the universe. This empirical result is far from trivial, for a cosmological constant would drive Rh(t) toward ct (t is the cosmic time) only once — and that would have to occur right now. Though we are not here espousing any particular alternative model of dark energy, for comparison we also consider scenarios in which dark energy is given by scaling solutions, which simultaneously eliminate several conundrums in the standard model, including the "coincidence" and "flatness" problems, and account very well for the fact that Rh(t0) ≈ ct0. [ABSTRACT FROM AUTHOR]