If the current energy density of the universe is indeed dominated by a
cosmological constant, then high-redshift sources will remain visible to us
only until they reach some finite age in their rest-frame. The radiation
emitted beyond that age will never reach us due to the acceleration of the
cosmic expansion rate, and so we will never know what these sources look like
as they become older. As a source image freezes on a particular time frame
along its evolution, its luminosity distance and redshift continue to increase
exponentially with observation time. The higher the current redshift of a
source is, the younger it will appear as it fades out of sight. For the popular
set of cosmological parameters, I show that a source at a redshift z=5-10 will
only be visible up to an age of 4-6 billion years. Arguments relating the
properties of high-redshift sources to present-day counterparts will remain
indirect even if we continue to monitor these sources for an infinite amount of
time. These sources will not be visible to us when they reach the current age
of the universe.Comment: Phys. Rev. D, in press (2001
