Consequences on variable Lambda-models from distant Type Ia supernovae and compact radio sources

Abstract

We study the m-z relation for Type Ia supernovae data and the θ-z relation for the updated compact radio sources data in 4 variable Λ- models: Λ\sim S^{-2}, Λ\sim H^2, Λ\sim ρand Λ\sim t^{-2}. It is found that all the models fit the data sets equally well and require non-zero, positive values of Λ. The supernovae data favour an accelerating expansion of the universe whereas the radio sources data imply either sign of the deceleration parameter. The estimates of the density parameter for the variable Λ-models are found higher than those for the constant Λ-Friedmann model. It is also found that the Gurvits et al' model (FRW model with Λ=0) is not the best-fitting model for the constant Λcase. The best-fitting Friedmann model (with constant Λ) is found to be a low density, vacuum-dominated accelerating universe. However, for realistic values of the matter density parameter, the only interesting solutions are (a) estimated from the supernovae data: the best-fit solutions for the flat models (including the constant Λcase); (b) estimated from the radio sources data: the global best-fit solutions for the models Λ\sim H^2 and Λ\sim ρ, the best-fit solution for the flat model with Λ=constant and the Gurvits et al' model. It is noted that, as in the case of recent CMB analyses, the data sets seem to favour a spherical universe (k>0).