Consequences on variable Lambda-models from distant type Ia supernovae andcompact radio sources

We study the magnitude-redshift relation for the type la supernovae data an d the angular size-redshift relation for the updated compact radio sources data (from Gurvits et al) by considering four variable Lambda -models: Lamb da similar to S-2, Lambda similar to H-2, Lambda similar to rho and Lambda similar to t(-2). It is found that all the variable Lambda -models, as well as the constant L ambda -Friedmann model, fit the supernovae data equally well with chi (2)/d of approximate to 1 and require non-zero, positive values of Lambda and an accelerating expansion of the universe. The estimates of the density parame ter for the variable h-models are found to be higher than those for the con stant Lambda -Friedmann model. From the compact radio sources data, it is found, by assuming the no-evolut ion hypothesis, that the Gurvits et al model (Friedmann model with Lambda = 0) is not the best-fitting model for the constant Lambda case. The best-fi tting Friedmann model (with constant Lambda) is found to be a low-density, vacuum-dominated accelerating universe. The fits of this data set to the (v ariable, as well as, constant Lambda-) models are found to be very good wit h chi (2)/dof approximate to 0.5 and require non-zero, positive values of L ambda with either sign of the deceleration parameter. However, for realisti c values of the matter density parameter, the only interesting solutions ar e (a) estimated from the supernovae data: the best-fitting solutions for th e flat models (including the constant Lambda case); (b) estimated from the radio sources data: the global best-fitting solutions for the models Lambda similar to H-2 and Lambda similar to rho, the best-fitting solution for th e flat model with Lambda = constant and the Gurvits ed al model. It is noted that, as in the case of recent cosmic microwave background anal yses, the data sets seem to favour a spherical universe (k > 0).