We are conducting a redshift survey of 177 flat-spectrum radio sources
in three samples covering the 5 GHz flux ranges 50 - 100, 100 - 200,
and 200 - 250 mJy. So far, we have measured 124 redshifts with complet
enesses of 80 %, 68 %, and 58 % for the bright, intermediate, and fain
t flux ranges. Using the newly determined redshift distribution, we ca
n derive cosmological limits from the statistics of the six gravitatio
nal lenses in the Jodrell Bank-VLA Astrometric Survey sample of 2500 h
at-spectrum radio sources brighter than 200 mJy at 5 GHz. For flat cos
mological models with a cosmological constant, the limit using only ra
dio data is Omega(0) > 0.27 at 2 sigma (0.47 < Omega(0) < 1.38 at 1 si
gma). The limits are statistically consistent with those for lensed qu
asars, and the combined radio + optical sample requires Omega(0) > 0.3
8 at 2 sigma (0.64 < Omega(0) < 1.66 at 1 sigma) for our most conserva
tive redshift completeness model, assuming that there are no quasar le
nses produced by spiral galaxies. Our best-fit model improves by appro
ximately 1 sigma if extinction in the early-type galaxies makes the le
nsed quasars fainter by Delta m = 0.58 +/- 0.45 mag, but we still find
a limit of Omega(0) > 0.26 at 2 sigma in flat cosmologies. The increa
sing fraction of radio galaxies as compared to quasars at fainter radi
o fluxes (rising from similar to 10 % at 1 Jy to similar to 50 % at 0.
1 Jy) explains why lensed optical emission is common for radio lenses
and partly explains the red color of radio-selected lenses.