The flat-spectrum radio luminosity function, gravitational lensing, galaxy ellipticities, and cosmology

The number of lenses found in the JVAS survey of flat-spectrum radio sources for gravitational lenses is consistent with statistical models of optical surveys for lensed quasars. The 90% confidence limit on Omega(0) in flat cosmological models (Omega(0) + lambda(0) = 1) is approximately 0.15 less than or similar to Omega(0) less than or similar to 2. Depending on the RLF model, we predict 2.4-3.6 lenses in the JVAS survey and in the first paper part of the fainter CLASS survey and 0.3-0.6 lenses in the brighter PHFS survey for an Omega(0) = 1 model. The uncertainties are because of the small numbers of lenses (there are only 4 compact JVAS lenses) and the uncertainties in the radio luminosity function (RLF) caused by the lack of information on the redshift distribution of 10-300 mJy radio sources. If we force the models to produce the observed number of JVAS lenses, the mean redshift of a 50 mJy source varies from z(s) = 0.4 for Omega(0) = 0, to 1.9 for Omega(0) = 1, to almost 4.0 for Omega(0) = 2 when Omega(0) + lambda(0) = 1. The source fluxes and redshifts of the lenses in the JVAS and CLASS surveys are consistent with the statistical models. The numbers of four-image lenses found in the JVAS survey and in surveys for lensed quasars are mutually consistent but slightly larger than expected for models using the observed axis ratios of E and SO galaxies. The best fts to the lens data require a projected axis ratio of b/a = 0.50 with a 90% confidence range of 0.25 < b/a < 0.65.