It took a heroic effort to measure the expansion rate of the universe. Hubble learned the difficulty of the measurement when he confused two types of Cepheid variable stars and got an expansion rate that was eight times too high. Since the inverse of the expansion rate is the age of the universe, his inferred age was just two billion years, younger than the age of the Earth! This was a crisis in astronomy for a while until the problem was understood. It took half a century and an effort involving dozens of astronomers and hundreds of nights of telescope time to measure the expansion rate to an accuracy of better than 10%.
As cosmology developed in the 1960s it was known that the gravity of all the galaxies in the universe should act to retard or slow down the initial expansion rate. The Hubble constant is not actually a constant; it's a parameter that has varied over cosmic time. It the tug of all the galaxies on each other has slowed down the expansion, that should be observable by extending the Hubble relation — the linear relationship or graph between galaxy distance and red shift & mdash: to larger distances and so larger look back times. Remember that distance light is old light, so higher red shift galaxies are seen as they were back in time, when the expansion rate should have been higher. In the 1970s and 1980s astronomers used large telescopes to try and trace the expansion history of the universe. Doing so would give a measure of the matter content of the universe. By the mid 1980s the answer seemed clear; the change in the expansion rate looking back in time was very small, indicating not nearly enough mass in the universe to overcome the initial expansion.
In the 1990's astronomers continued this work, using supernovae as distance indicators. The super vovae that result from mass transfer in a binary system are extremely useful in cosmology, because the peak brightness of the supernova yields a distance estimate accurate to about 15%, and the supernova is bright enough to outshine its entire galaxy and be seen to distances of 5-8 billion light years. The result of this work was a huge surprise! Instead of appearing brighter relative to the expectation for a model with no change in expansion rate (deceleration over time making them closer than expected), the supernovae were fainter (indicating they were further away than expected). This unanticipated faintness of the distant supernovae was interpreted as an acceleration of the expanding universe over the past five billion years. Gravity could only make the expansion rate slow down; this was something with the opposite property to gravity. Research groups led by Saul Perlmutter, Adam Riess, and Brian Schmidt did this research, and their discovery of the accelerating universe won them a Nobel Prize in 2011.
The expansion history of the universe is an extremely important diagnostic of the contents of the universe. The universe begans 13.8 billion years ago, in an exceptionally hot and dense state called the big bang. The initial expansion rate was extremely rapid. Then it slowed down due to the influence of matter, primarily dark matter. About five billion years ago the expansion rate began to increase, as the ingredient that astronomers call dark energy became dominant. As far as we know, the expansion rate will continue to increase in the future, driving galaxies apart at ever-increasing rates.
The most distant galaxies whose light we can gather are at a distance of 46 billion light years. This sounds wrong — how can there be galaxies this far away in a universe only 13.8 billion years old? The answer is that the universe was expanding faster than light for much of its early history. That is, the distance between any two points in expanding space-time was increasing at faster than light speed. So there are regions of the universe we have never seen, because the light has not been able to reach us in the entire history of the universe. Due to deceleration, some of those regions came into view. As the universe got older, more and more distant regions became observable. But recently the expansion rate has been increasing and some galaxies whose light we saw will in the future be removed from view. The universe is stranger and more amazing than we could possibly imagine!