Journal Article

The angular-diameter distance maximum and its redshift as constraints on Λ≠ 0 Friedmann–Lemaître–Robertson–Walker models

Marcelo E. Araújo and William R. Stoeger

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 394, issue 1, pages 438-442
Published in print March 2009 | ISSN: 0035-8711
Published online March 2009 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2008.14321.x
The angular-diameter distance maximum and its redshift as constraints on Λ≠ 0 Friedmann–Lemaître–Robertson–Walker models

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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 zmax– as is already known but rarely recognized – the redshift of Cmax, the maximum of the angular-diameter distance, uniquely gives ΩΛ, the amount of vacuum energy in the universe, independent of H0, the Hubble parameter. For non-flat models, determination of both zmax and Cmax gives both ΩΛ and ΩM, the amount of matter in the universe, as long as we know H0 independently. Finally, determination of Cmax automatically gives a very simple observational criterion for whether or not the universe is flat – presuming that it is FLRW.

Keywords: cosmological patterns; cosmology: theory

Journal Article.  3925 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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