When Albert Einstein formulated General Relativity in 1915, he was not aware the Universe was expanding. Large scale structure in the form of galaxies was not known and all fuzzy luminous nebulae were considered basically similar and within stellar distance scales. Only with Hubble work in 1930 came the realization some of those nebulae were in fact island universes, and that they were not only very far, but also receding from us at enormous speeds.
This was not known for Einstein, and since gravitation exerts its influence up to infinity, it was natural for him to postulate some force working in the preservation of an apparent equilibrium among matter, preventing universal collapse. This is why he postulated the Cosmological Constant, symbolized by the Greek letter Lambda, and included a term accounting for it in the field equations.
Once universal expansion was discovered, the need for an unknown repulsive agent could be dropped and Einstein dismissed the Cosmological Constant as his "biggest blunder".
Weighting the Universe
The cosmological problem thereafter, focused on determining the nature of universal expansion, whether it should continue forever, whether it should tend to stabilize, or reverse and end in a "Big Crunch".
To answer the fundamental question, it was necessary to undertake a comprehensive census of matter. With this data it should be possible to compute the overall effect of gravitation and - in concert with the observed expansion rate - determine the Universe's ultimate fate. With enough matter, its gravitational tug should be capable of braking expansion either asimptotically at infinite, or even reverse it.
Census of visible matter (stars, dust, hydrogen clouds) turned out to be about 3% of the critical amount needed for a closed Universe, but the existence of some form of "dark matter" was strongly hinted by observation of the speed distribution of stars orbiting different regions of spiral galaxies. According to regular mechanics, objects farther from galactic center should exhibit decreasing angular speed in comparison with those closer in, just as outer planets take longer to complete an orbit around the Sun as compared with the inner ones.
This was not observed, in fact, angular speeds appeared essentially uniform as if galactic disks were behaving more or less like rigid entities. The discrepancy could be reconciled with the assumption of some form of invisible matter engulfing them, pulling visible matter together under its influence and creating the illusion of a rigidly rotating unit.
The case for dark matter has been further boosted by direct observation of yet another General Relativity prediction, the gravitational lensing of light rays by massive objects. Several examples of gravitational lenses are well documented, and the phenomenon is now being exploited to map albeit coarsely, cosmic distribution of dark matter under favorable circumstances.
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