A lower limit on Ωm-ΩΛ using gravitational lensing in the Hubble Deep Field

We calculate the expected number of multiply imaged galaxies in the Hubble Deep Field (HDF), using photometric redshift information for galaxies with m(I) < 27 that were detected in all four HDF passbands. A comparison of these expectations with the observed number of strongly lensed galaxies places a lower limit on the current value of Omega(m) - Omega(Lambda), where Omega(m) is the cosmological mass density of the universe and Omega(Lambda) is the normalized cosmological constant. Based on current estimates of the HDF luminosity function and associated uncertainties in individual parameters, our 95% confidence lower limit on Omega(m) - Omega(Lambda) is between -0.44, if there are no strongly lensed galaxies in the HDF, and -0.73, if there are two strongly lensed galaxies in the HDF. For a flat universe (Omega(m) + Omega(Lambda) = 1), Omega(Lambda) < 0.58-0.79 (95% confidence limit). If the only lensed galaxy in the HDF is the one presently viable candidate, then in a flat universe (Omega(m) + Omega(Lambda) = 1), Omega(Lambda) < 0.79 (95% confidence limit). These lower limits are compatible with estimates based on high-redshift supernovae and with previous limits based on gravitational lensing.