The time that Einstein set to discover "dark energy", and almost discovered "dark matter" instead. THREAD

In 1921, Einstein was pondering the question of whether the universe is spatially finite or not. A question, he argued, that is "entirely meaningful in the sense of practical geometry" https://einsteinpapers.press.princeton.edu/vol7-trans/231 

Einstein thought that the cosmological constant term, that he had himself introduced a few years earlier, could manifest itself as a "mass-density of negative sign, distributed uniformly throughout space" https://einsteinpapers.press.princeton.edu/vol7-trans/232 

If one could measure the statistical distribution and masses of stars in the Milky Way -- which as far as Einstein and everyone else knew in 1921 corresponded to the whole universe! -- then by Newton’s law one could calculate the average velocities of stars, assuming equilibrium

If the measured velocities of stars were smaller than predicted -- Einstein thought -- we would prove the existence of a negative mass density, and, indirectly, that the universe is finite. In fact, one would be able to estimate its size!

But too little was known in 1921 about the size of the Milky Way and the statistical properties of its stellar population, and Einstein concluded that the average mass-density in the universe was "a quantity of which there is no knowledge" https://www.nytimes.com/1921/05/14/archives/einstein-cannot-measure-universe-with-mean-density-of-matter.html

Einstein then considered a spherical star cluster, and applied the virial theorem to establish a connection between the velocity dispersion of stars and their mean density https://einsteinpapers.press.princeton.edu/vol7-trans/246 

Einstein found a rough agreement between observed and predicted velocities, and therefore could not say much about the presence of a negative mass-density in the cluster

He did go beyond that conclusion however, and argued that "the non luminous masses contribute no higher order of magnitude to the total mass than the luminous masses". In other words: he set an upper limit on the amount of dark matter in the cluster https://einsteinpapers.press.princeton.edu/vol7-trans/249 

Einstein was too ahead of its time. In the following years, the existence of galaxies outside of our own will be discovered. In 1933, Fritz Zwicky will make use of exactly the same method to claim the presence of dark matter in galaxy clusters http://ned.ipac.caltech.edu/level5/March17/Zwicky/frames.html

Many thanks to Tom Richtler for pointing out Einstein's 1921 paper "A Simple Application of the Newtonian Law of Gravitation to Globular Star Clusters"

For more information about the history of dark matter see: https://arxiv.org/abs/1605.04909  with @DanHooperAstro