
TL;DR
This paper compares different metric formulations of the universe's spacetime, linking horizons in these models to observational data, and clarifies the limits of our observable universe based on cosmic curvature.
Contribution
It introduces a dual metric approach to cosmic spacetime, connecting horizons in comoving and observer-dependent frames, and applies recent WMAP data for precise curvature calculations.
Findings
The Rindler event horizon coincides with the curvature horizon in observer-dependent coordinates.
The cosmic horizon's size depends on the universe's matter-energy content and its evolution.
In a de Sitter universe, the horizon remains fixed over time.
Abstract
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…
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