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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 Ω m -Ω Λ , where Ω m is the cosmological mass density of the universe and Ω Λ 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 Ω m -Ω Λ 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 (Ω m +Ω Λ =1), Ω Λ <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 (Ω m +Ω Λ =1), Ω Λ <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.
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Cooray et al. (1999) studied this question.
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