Luminous extragalactic water masers are known to be associated with AGN and have provided accurate estimates for the mass of the central supermassive black hole and the size and structure of the accretion disk in nearby galaxies. To find water masers at much higher redshifts, we have begun a survey of known gravitationally lensed quasars and star-forming galaxies. In this paper, we present a search for 22 GHz (rest frame) water masers toward five dusty, gravitationally lensed quasars and star-forming galaxies at redshifts 2.3--2.9 with the Effelsberg telescope and the EVLA. Our observations do not find any new definite examples of high redshift water maser galaxies, suggesting that large reservoirs of dust and gas are not a sufficient condition for powerful water maser emission. However, we do find the tentative detection of a water maser system in the active galaxy IRAS 10214+4724 at redshift 2.285. Our survey has now doubled the number of lensed galaxies and quasars that have been searched for high redshift water masers. We present an analysis of the high redshift water maser luminosity function that is based on the results presented here and from the only cosmologically distant (z > 1) water maser galaxy found thus far, MG J0414+0534 at redshift 2.64. By comparing with the luminosity function locally and at moderate redshifts, we find that there must be some evolution in the luminosity function of water maser galaxies at high redshifts. By assuming a moderate evolution [(1 + z )^4] in the luminosity function, we find that blind surveys for water maser galaxies are only worthwhile with extremely high sensitivity like that of the planned Square Kilometre Array. However, instruments like the EVLA and MeerKAT will be capable of detecting water maser systems similar to the one found from MG J0414+0534 through targeted observations.
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