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In the standard cosmological model, the merger remnant of the Milky Way and Andromeda (Milkomeda) will be the only galaxy remaining within our event horizon once the Universe has aged by another factor of ten, ~10^11 years after the Big Bang. After that time, the only extragalactic sources of light in the observable cosmic volume will be hypervelocity stars being ejected continuously from Milkomeda. Spectroscopic detection of the velocity-distance relation or the evolution in the Doppler shifts of these stars will allow a precise measurement of the vacuum mass density as well as the local matter distribution. Already in the near future, the next generation of large telescopes will allow photometric detection of individual stars out to the edge of the Local Group, and may target the ~10^5+-1 hypervelocity stars that originated in it as cosmological tracers.
Abraham Loeb (Mon,) studied this question.
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