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

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 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 C max 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. © 2009 RAS.