A study of the angular size-redshift relation for models in which $\Lambda$ decays as the energy density

By modifying the Chen and Wu ansatz, we have investigated some Friedmann models in which $\Lambda$ varies as $\rho$. In order to test the consistency of the models with observations, we study the angular size - redshift relation for 256 ultracompact radio sources selected by Jackson and Dodgson. The angular sizes of these sources were determined by using very long-baseline interferometry in order to avoid any evolutionary effects. The models fit the data very well and require an accelerating universe with a positive cosmological constant. Open, flat and closed models are almost equally probable, though the open model provides a comparatively better fit to the data. The models are found to have intermediate density and imply the existence of dark matter, though not as much as in the canonical Einstein-de Sitter model.