The cosmic horizon
Abstract
The cosmological principle, promoting the view that the Universe is homogeneous and isotropic, is embodied within the mathematical structure of the RobertsonWalker (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 timedependent expansion factor. These coordinates, however, do not explicitly reveal the 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 observerdependent coordinates  first for the wellknown 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 comoving system  coincides with what one might call the `curvature horizon' appearing in the observerdependent frame. The advantage of this dual prescription of the cosmic spacetime is that with the latest Wilkinson Microwave Anisotropy Probe results, we now have a much better determination of the Universe's massenergy content, which permits us to calculate this curvature with unprecedented accuracy. We use it here to demonstrate that our observations have probed the limit beyond which the cosmic curvature prevents any signal from having ever reached us. In the case of de Sitter, where the massenergy density is a constant, this limit is fixed for all time. For a universe with a changing density, this horizon expands until de Sitter is reached asymptotically, and then it too ceases to change.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 December 2007
 DOI:
 10.1111/j.13652966.2007.12499.x
 arXiv:
 arXiv:0711.4181
 Bibcode:
 2007MNRAS.382.1917M
 Keywords:

 cosmic microwave background;
 cosmological parameters;
 cosmology: observations;
 cosmology: theory;
 distance scale;
 Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 Accepted for publication in MNRAS