Consequences on variable Λ-models from distant type Ia supernovae and compact radio sources

We study the magnitude-redshift relation for the type Ia supernovae data and the angular size-redshift relation for the updated compact radio sources data (from Gurvits et al ) by considering four variable Λ-models: Λ~ S -2 , Λ~ H 2 , Λ~ρ and Λ~ t -2 . It is found that all the variable Λ-models, as well as the constant Λ-Friedmann model, fit the supernovae data equally well with χ 2 / dof ≈1 and require non-zero, positive values of Λ and an accelerating expansion of the universe. The estimates of the density parameter for the variable Λ-models are found to be higher than those for the constant Λ-Friedmann model. From the compact radio sources data, it is found, by assuming the no-evolution hypothesis, that the Gurvits et al model (Friedmann model with Λ = 0) is not the best-fitting model for the constant Λ case. The best-fitting Friedmann model (with constant Λ) is found to be a low-density, vacuum-dominated accelerating universe. The fits of this data set to the (variable, as well as, constant Λ-) models are found to be very good with χ 2 / dof ≈0.5 and require non-zero, positive values of Λ with either sign of the deceleration parameter. However, for realistic values of the matter density parameter, the only interesting solutions are (a) estimated from the supernovae data: the best-fitting solutions for the flat models (including the constant Λ case); (b) estimated from the radio sources data: the global best-fitting solutions for the models Λ~ H 2 and Λ~ρ, the best-fitting solution for the flat model with Λ = {}constant and the Gurvits et al model. It is noted that, as in the case of recent cosmic microwave background analyses, the data sets seem to favour a spherical universe ( k >0).