The angular-diameter distance maximum and its redshift as constraints on Λ≠ 0 Friedmann–Lemaître–Robertson–Walker models |
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| Authors: | Marcelo E Araújo William R Stoeger |
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| Institution: | Departamento de Física-Matemática, Instituto de Física, Universidade do Brasil, 21.945-970, Rio de Janeiro, RJ, Brazil;Vatican Observatory Research Group, Steward Observatory, 933 North Cherry Avenue, The University of Arizona, Tucson, AZ 85721, USA |
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| Abstract: | The plethora of recent cosmologically relevant data has indicated that our Universe is very well fitted by a standard Friedmann–Lemaître–Robertson–Walker (FLRW) model, with  and ΩΛ≈ 0.73 – or, more generally, by nearly flat FLRW models with parameters close to these values. Additional independent cosmological information, particularly the maximum of the angular-diameter (observer area) distance and the redshift at which it occurs, would improve and confirm these results, once sufficient precise Type Ia supernovae data in the range 1.5 < z < 1.8 become available. We obtain characteristic FLRW-closed functional forms for C = C ( z ) and  , the angular-diameter distance and the density per source counted, respectively, when Λ≠ 0 , analogous to those we have for Λ= 0 . More importantly, we verify that for flat FLRW models z max– as is already known but rarely recognized – the redshift of C max, the maximum of the angular-diameter distance, uniquely gives ΩΛ , the amount of vacuum energy in the universe, independent of H 0, the Hubble parameter. For non-flat models, determination of both z max and C max gives both ΩΛ and ΩM, the amount of matter in the universe, as long as we know H 0 independently. Finally, determination of C max automatically gives a very simple observational criterion for whether or not the universe is flat – presuming that it is FLRW. |
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| Keywords: | cosmological patterns cosmology: theory |
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