Implications of a Nonzero Cosmological Constant and Luminosity Selection Effects on Cosmological Tests

Abstract

This paper examines the implications of a nonzero cosmological constant Λ ₀ on the amount of linear size evolution and the luminosity selection effects usually required in the interpretation of the angular diameter–redshift (θ–z) test. This is based on three typical cases chosen on various plausible assumptions which can be made concerning the contribution of Λ ₀ to the density of the universe (parametrised by &OHgr;₀). The results show that a fairly strong linear size evolution will be required to interpret the θ–z data of extended steep spectrum quasars for all three cases, if luminosity effects are neglected. However, this evolution is significantly steeper in a matter-dominated universe with &OHgr;_M = &OHgr;₀ = 1 than in both the flat universe with &OHgr;Λ = 0·8, &OHgr;_M = 0·2 and an open universe with &OHgr;_M = 0·2, Λ = 0.

Furthermore, when the luminosity selection effects present in the sample are considered, a milder size evolution is obtained for the &OHgr;_M = 1, &OHgr;Λ = 0 model while little or no size evolution is found for the other two cases. There is therefore no significant difference in our results for an open low density universe with &OHgr;Λ = 0 and a flat universe dominated by &OHgr;Λ predicted by inflation. The present results therefore imply that an open low density universe with &OHgr;_M = 0·2 and &OHgr;Λ = 0 is compatible with an inflationary model of the universe with &OHgr;_M = 0·2 and &OHgr;Λ = 0 · 8. This leads to a contradiction since the universe cannot be open and spatially closed at the same time (the existence of one should preclude the other).