A Lower Limit on Omega-Lambda Using Gravitational Lensing in the Hubble Deep Field

Abstract

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. 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% C.L.). These lower limits are compatible with estimates based on high-redshift supernovae and with previous limits based on gravitational lensing.