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Powerful extended radio galaxies in the 3CR survey are observed out toredshifts of about 2. For redshifts greater than about 0.3, the averagelobe-lobe size of the sources decreases monotonically with redshift for allreasonable cosmological parameter choices. This suggests that thecharacteristic time for which an AGN produces a highly collimated outflow thatpowers the radio emission is shorter for the high-redshift sources than it isfor low-redshift sources. The fact that the characteristic time for which anAGN produces a collimated outflow decreases with redshift implies that thephysical mechanism that gives rise to the large scale jets is not Eddingtonlimited. Higher redshift sources have higher radio powers due the flux limit ofthe sample, and sources with higher radio powers have higher beam powersrelative to lower redshift sources. Both the beam power and active lifetime ofthe AGN are controlled by processes occurring at the heart of the AGN, and maybe related for non-Eddington limited processes. The relation between the activelifetime, $t_*$, and the beam power, $L_j$, of powerful extended radio galaxiesis investigated here and found to be $t_*\proptoL_j^{-2/3}$. A comparison ofthe redshift evolution of the characteristic source sizes with that of theaverage lobe-lobe size for the 3CR sample of radio galaxies could be used toconstrain cosmology.Comment: revised version accepted to ApJ, in press, Vol 49

Central Engines of Active Galactic Nuclei: Properties of Collimated Outflows and Applications for Cosmology