Proper size of the visible Universe in FRW metrics with a constant spacetime curvature
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Publication:2851372
DOI10.1088/0264-9381/30/15/155007zbMATH Open1273.83192arXiv1207.1332OpenAlexW2087901061WikidataQ56979837 ScholiaQ56979837MaRDI QIDQ2851372
Publication date: 10 October 2013
Published in: Classical and Quantum Gravity (Search for Journal in Brave)
Abstract: In this paper, we continue to examine the fundamental basis for the Friedmann-Robertson-Walker (FRW) metric and its application to cosmology, specifically addressing the question: What is the proper size of the visible universe? There are several ways of answering the question of size, though often with an incomplete understanding of how far light has actually traveled in reaching us today from the most remote sources. The difficulty usually arises from an inconsistent use of the coordinates, or an over-interpretation of the physical meaning of quantities such as the so-called proper distance R(t)=a(t)r, written in terms of the (unchanging) co-moving radius r and the universal expansion factor a(t). In this paper, we use the five non-trivial FRW metrics with constant spacetime curvature (i.e., the static FRW metrics, but excluding Minkowski) to prove that in static FRW spacetimes in which expansion began from an initial signularity, the visible universe today has a proper size equal 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-existing positions away from the origin. In so doing, we confirm earlier results showing the same phenomenon in a broad range of cosmologies, including LCDM, based on the numerical integration of null geodesic equations through an FRW metric.
Full work available at URL: https://arxiv.org/abs/1207.1332
Relativistic cosmology (83F05) Equations of motion in general relativity and gravitational theory (83C10) General questions in astronomy and astrophysics (85A04) Astrophysical cosmology (85A40)
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