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The Angular-Diameter Distance Maximum as an Independent Test of the Flat FLRW Standard Cosmology

May, 2007
5 pages
Published in:
  • Mon.Not.Roy.Astron.Soc. 394 (2009) 438-442
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Abstract: (arXiv)
The plethora of recent cosmologically relevant data has indicated that our universe is very well fit by a standard Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) model, with ΩM≈0.27\Omega_{M} \approx 0.27 and ΩΛ≈0.73\Omega_{\Lambda} \approx 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 Supernovae Ia data in the range 1.5<z<1.81.5 < z < 1.8 become available. We obtain characteristic FLRW closed functional forms for C=C(z)C = C(z) and M^0=M^0(z)\hat{M}_0 = \hat{M}_0(z), the angular-diameter distance and the density per source counted, respectively, when Λ≠0\Lambda \neq 0, analogous to those we have for Λ=0\Lambda = 0. More importantly, we verify that for flat FLRW models zmaxz_{max} -- as is already known but rarely recognized -- the redshift of CmaxC_{max}, the maximum of the angular-diameter-distance, uniquely gives ΩΛ\Omega_{\Lambda}, the amount of vacuum energy in the universe, independently of H0H_0, the Hubble parameter. For non-flat models determination of both zmaxz_{max} and CmaxC_{max} gives both ΩΛ\Omega_{\Lambda} and ΩM\Omega_M, the amount of matter in the universe, as long as we know H0H_0 independently. Finally, determination of CmaxC_{max} automatically gives a very simple observational criterion for whether or not the universe is flat -- presuming that it is FLRW.