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In this paper, we continue to examine the fundamental basis for theFriedmann-Robertson-Walker (FRW) metric and its application to cosmology,specifically addressing the question: What is the proper size of the visibleuniverse? There are several ways of answering the question of size, thoughoften with an incomplete understanding of how far light has actually traveledin reaching us today from the most remote sources. The difficulty usuallyarises from an inconsistent use of the coordinates, or an over-interpretationof the physical meaning of quantities such as the so-called proper distanceR(t)=a(t)r, written in terms of the (unchanging) co-moving radius r and theuniversal expansion factor a(t). In this paper, we use the five non-trivial FRWmetrics with constant spacetime curvature (i.e., the static FRW metrics, butexcluding Minkowski) to prove that in static FRW spacetimes in which expansionbegan from an initial signularity, the visible universe today has a proper sizeequal to R_h(t_0/2), i.e., the gravitational horizon at half its current age.The exceptions are de Sitter and Lanczos, whose contents had pre-existingpositions away from the origin. In so doing, we confirm earlier results showingthe same phenomenon in a broad range of cosmologies, including LCDM, based onthe numerical integration of null geodesic equations through an FRW metric.

Proper Size of the Visible Universe in FRW Metrics with Constant Spacetime Curvature