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The Cosmic Horizon

The cosmological principle, promoting the view that the universe is homogeneous and isotropic, is embodied within the mathematical structure of the Robertson-Walker (RW) metric. The equations derived from an application of this metric to the Einstein Field Equations describe the expansion of the universe in terms of comoving coordinates, from which physical distances may be derived using a time-dependent expansion factor. These coordinates, however, do not explicitly reveal properties of the cosmic spacetime manifested in Birkhoff's theorem and its corollary. In this paper, we compare two forms of the metric--written in (the traditional) comoving coordinates, and a set of observer-dependent coordinates--first for the well-known de Sitter universe containing only dark energy, and then for a newly derived form of the RW metric, for a universe with dark energy and matter. We show that Rindler's event horizon--evident in the co-moving system--coincides with what one might call the "curvature horizon" appearing in the observer-dependent frame. The advantage of this dual prescription of the cosmic spacetime is that with the latest WMAP results, we now have a much better d