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

Abstract

We study the magnitude-redshift relation for the Type Ia super- novae 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 ∼ H2 , 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 χ2 /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 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 very good with χ2 /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-fit solutions for the flat models (including the constant Λ case); (b) estimated from the radio sources data: the global best-fit solutions for the models Λ ∼ H2 and Λ ∼ 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).